CBSE Physics Class XII Short Look

 CBSE Physics Class XII 

Unit I: Electrostatics 26 Periods
Chapter–1: Electric Charges and Fields
Electric charges, Conservation of charge, Coulomb's law-force between
two- point charges, forces between multiple charges; superposition principle
and continuous charge distribution.
Electric field, electric field due to a point charge, electric field lines, electric
dipole, electric field due to a dipole, torque on a dipole in uniform electric
field.
Electric flux, statement of Gauss's theorem and its applications to find field
due to infinitely long straight wire, uniformly charged infinite plane sheet
and uniformly charged thin spherical shell (field inside and outside).
Chapter–2: Electrostatic Potential and Capacitance
Electric potential, potential difference, electric potential due to a point
charge, a dipole and system of charges; equipotential surfaces, electrical
potential energy of a system of two-point charges and of electric dipole in
an electrostatic field.
Conductors and insulators, free charges and bound charges inside a
conductor. Dielectrics and electric polarization, capacitors and capacitance,
combination of capacitors in series and in parallel, capacitance of a parallel
plate capacitor with and without dielectric medium between the plates,
energy stored in a capacitor (no derivation, formulae only).
Unit II: Current Electricity 18 Periods
Chapter–3: Current Electricity
Electric current, flow of electric charges in a metallic conductor, drift
velocity, mobility and their relation with electric current; Ohm's law, V-I
characteristics (linear and non-linear), electrical energy and power,
electrical resistivity and conductivity, temperature dependence of
resistance, Internal resistance of a cell, potential difference and emf of a
cell, combination of cells in series and in parallel, Kirchhoff's rules,
Wheatstone bridge.
Unit III: Magnetic Effects of Current and Magnetism 25 Periods
Chapter–4: Moving Charges and Magnetism
Concept of magnetic field, Oersted's experiment.
Biot - Savart law and its application to current carrying circular loop.
Ampere's law and its applications to infinitely long straight wire. Straight
solenoid (only qualitative treatment), force on a moving charge in uniform
magnetic and electric fields.
Force on a current-carrying conductor in a uniform magnetic field, force
between two parallel current-carrying conductors-definition of ampere,
torque experienced by a current loop in uniform magnetic field; Current loop
as a magnetic dipole and its magnetic dipole moment, moving coil
galvanometer- its current sensitivity and conversion to ammeter and
voltmeter.
Chapter–5: Magnetism and Matter
Bar magnet, bar magnet as an equivalent solenoid (qualitative treatment
only), magnetic field intensity due to a magnetic dipole (bar magnet) along
its axis and perpendicular to its axis (qualitative treatment only), torque on a
magnetic dipole (bar magnet) in a uniform magnetic field (qualitative
treatment only), magnetic field lines.
Magnetic properties of materials- Para-, dia- and ferro -
magnetic substances with examples, Magnetization of materials,
effect of temperature on magnetic properties.
Unit IV: Electromagnetic Induction and Alternating Currents 24 Periods
Chapter–6: Electromagnetic Induction
Electromagnetic induction; Faraday's laws, induced EMF and current;
Lenz's Law, Self and mutual induction.
Chapter–7: Alternating Current
Alternating currents, peak and RMS value of alternating current/voltage;
reactance and impedance; LCR series circuit (phasors only), resonance,
power in AC circuits, power factor, wattless current.
AC generator, Transformer.
Unit V: Electromagnetic waves 04 Periods
Chapter–8: Electromagnetic Waves
Basic idea of displacement current, Electromagnetic waves, their
characteristics, their transverse nature (qualitative idea only).
Electromagnetic spectrum (radio waves, microwaves, infrared, visible,
ultraviolet, X-rays, gamma rays) including elementary facts about their uses.
Unit VI: Optics 30 Periods
Chapter–9: Ray Optics and Optical Instruments
Ray Optics: Reflection of light, spherical mirrors, mirror formula, refraction
of light, total internal reflection and optical fibers, refraction at spherical
surfaces, lenses, thin lens formula, lens maker’s formula, magnification,
power of a lens, combination of thin lenses in contact, refraction of light
through a prism.
Optical instruments: Microscopes and astronomical telescopes (reflecting
and refracting) and their magnifying powers.
Chapter–10: Wave Optics
Wave optics: Wave front and Huygen’s principle, reflection and refraction
of plane wave at a plane surface using wave fronts. Proof of laws of
reflection and refraction using Huygen’s principle. Interference, Young's
double slit experiment and expression for fringe width (No derivation final
expression only), coherent sources and sustained interference of light,
diffraction due to a single slit, width of central maxima (qualitative treatment
only).
Unit VII: Dual Nature of Radiation and Matter 08 Periods
Chapter–11: Dual Nature of Radiation and Matter
Dual nature of radiation, Photoelectric effect, Hertz and Lenard's
observations; Einstein's photoelectric equation-particle nature of light.
Experimental study of photoelectric effect
Matter waves-wave nature of particles, de-Broglie relation.
Unit VIII: Atoms and Nuclei 15 Periods
Chapter–12: Atoms
Alpha-particle scattering experiment; Rutherford's model of atom; Bohr
model of hydrogen atom, Expression for radius of nth possible orbit, velocity
and energy of electron in nth orbit, hydrogen line spectra (qualitative
treatment only).
Chapter–13: Nuclei
Composition and size of nucleus, nuclear force
Mass-energy relation, mass defect; binding energy per nucleon and its
variation with mass number; nuclear fission, nuclear fusion.
Unit IX: Electronic Devices 10 Periods
Chapter–14: Semiconductor Electronics: Materials, Devices and
Simple Circuits
Energy bands in conductors, semiconductors and insulators (qualitative
ideas only) Intrinsic and extrinsic semiconductors- p and n type, p-n junction
Semiconductor diode - I-V characteristics in forward and reverse
bias, application of junction diode -diode as a rectifier.

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Electric Charges and Fields

1. Electric Charges

• A charge is a fundamental property of matter that causes it to experience a force in an electric field.
• There are two types of charges:
  • Positive charge (proton)
  • Negative charge (electron)
• Like charges repel, unlike charges attract.

2. Conservation of Charge

• Charge can neither be created nor destroyed, only transferred from one body to another.
• Total charge in an isolated system remains constant.

3. Coulomb’s Law

• It gives the force between two point charges.
• Formula: $$F = \frac{k q_1 q_2}{r^2}$$ where:
  • $F$ = Electrostatic force
  • $k = 9 \times 10^9 \, \text{N m}^2/\text{C}^2$ (Coulomb’s constant)
  • $q_1, q_2$ = Magnitudes of two charges
  • $r$ = Distance between the charges

4. Superposition Principle

• When multiple charges are present, the net force on any charge is the vector sum of forces due to all other charges.

5. Continuous Charge Distribution

• Charge is spread over a line, surface, or volume instead of being at a point.

---

Electric Field

• Electric Field (E): The force experienced per unit charge at a point.
• Formula: $$E = \frac{F}{q}$$
  • Unit: N/C or V/m
• Electric Field Due to a Point Charge: $$E = \frac{k q}{r^2}$$
• Electric Field Lines:
  • Imaginary lines showing the direction of the electric field.
  • Start from positive and end at negative charges.
  • Never intersect.

---

Electric Dipole

• Two equal and opposite charges separated by a small distance form a dipole.
• Dipole Moment (p): $$p = q \times d$$ where $d$ is the distance between the charges.

Electric Field Due to a Dipole

• On axial line: $$E = \frac{2k p}{r^3}$$
• On equatorial line: $$E = \frac{k p}{r^3}$$

Torque on a Dipole in Uniform Electric Field

• Formula: $$\tau = pE \sin \theta$$
  • Max torque when $\theta = 90^\circ$.

---

Electric Flux ($\Phi$)

• It measures the total electric field passing through a surface.
• Formula: $$\Phi = E A \cos \theta$$
  • Unit: Nm²/C

Gauss’s Theorem

• The total electric flux through a closed surface is equal to $$\frac{1}{\varepsilon_0} \times \text{(total charge enclosed)}$$ where $\varepsilon_0$ is the permittivity of free space.

---

Applications of Gauss’s Theorem

1. Electric Field Due to an Infinitely Long Straight Wire

   $$E = \frac{\lambda}{2\pi \varepsilon_0 r}$$
   • $\lambda$ = Charge per unit length
   • $r$ = Distance from the wire

2. Electric Field Due to a Uniformly Charged Infinite Plane Sheet

   $$E = \frac{\sigma}{2\varepsilon_0}$$
   • $\sigma$ = Surface charge density

3. Electric Field Due to a Uniformly Charged Thin Spherical Shell

   • Outside the shell: Acts like a point charge $$E = \frac{kQ}{r^2}$$
   • Inside the shell: $E = 0$ (No field inside a charged spherical shell)
   • ======================================================

   • 1. Electric Potential

   • Electric Potential (V): The electric potential at a point is the work done to bring a unit positive charge from infinity to that point.
   • Formula: $$V = \frac{W}{q}$$
     • Unit: Volt (V)
     • 1 Volt = 1 Joule/Coulomb

   ---

   2. Potential Difference

4. The difference in electric potential between two points.
5. Formula: $$V_B - V_A = \frac{W}{q}$$
   • Work done per unit charge to move the charge from $A$ to $B$.

---

3. Electric Potential Due to:

• A Point Charge: $$V = \frac{k q}{r}$$
• A Dipole (At Axial and Equatorial Points): $$V = \frac{k p \cos\theta}{r^2}$$
• A System of Charges:
  • The total potential at a point due to multiple charges is the algebraic sum of the potentials due to individual charges.
  $$V = V_1 + V_2 + V_3 + \dots$$

---

4. Equipotential Surfaces

• A surface where the electric potential is constant at all points.
• Properties:
  • No work is done when moving a charge on an equipotential surface.
  • Equipotential surfaces are perpendicular to electric field lines.

---

5. Electrical Potential Energy

• The potential energy of a system of charges is the work done in assembling the charges.
• For Two-Point Charges: $$U = \frac{k q_1 q_2}{r}$$
• For an Electric Dipole in an External Field: $$U = - pE \cos\theta$$

---

6. Conductors and Insulators

• Conductors: Allow free movement of charges (e.g., metals).
• Insulators: Do not allow free charge movement (e.g., rubber, glass).

---

7. Free and Bound Charges

• Free Charges: Move freely inside a conductor.
• Bound Charges: Stay attached to atoms in insulators.

---

8. Dielectrics and Polarization

• Dielectric: An insulating material placed between capacitor plates.
• Polarization: Alignment of molecular dipoles in response to an electric field, reducing the effective field inside the material.

---

9. Capacitors and Capacitance

• Capacitor: A device used to store charge and energy.
• Capacitance (C): Ability of a capacitor to store charge. $$C = \frac{Q}{V}$$
  • Unit: Farad (F)

Parallel Plate Capacitor

• Without Dielectric: $$C = \frac{\varepsilon_0 A}{d}$$
• With Dielectric: $$C = \frac{K \varepsilon_0 A}{d}$$
  • $K$ = Dielectric constant

---

10. Combination of Capacitors

• Series Combination: $$\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \dots$$
• Parallel Combination: $$C_{\text{eq}} = C_1 + C_2 + C_3 + \dots$$

---

11. Energy Stored in a Capacitor

$$U = \frac{1}{2} C V^2$$ $$U = \frac{1}{2} Q V$$ $$U = \frac{Q^2}{2C}$$                              

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Chapter 3:

Electric Potential and Capacitance - Class 12 Physics (CBSE) Notes

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1. Electric Potential

• Electric Potential (V): The electric potential at a point is the work done to bring a unit positive charge from infinity to that point.
• Formula: $$V = \frac{W}{q}$$
  • Unit: Volt (V)
  • 1 Volt = 1 Joule/Coulomb

---

2. Potential Difference

• The difference in electric potential between two points.
• Formula: $$V_B - V_A = \frac{W}{q}$$
  • Work done per unit charge to move the charge from $A$ to $B$.

---

3. Electric Potential Due to:

• A Point Charge: $$V = \frac{k q}{r}$$
• A Dipole (At Axial and Equatorial Points): $$V = \frac{k p \cos\theta}{r^2}$$
• A System of Charges:
  • The total potential at a point due to multiple charges is the algebraic sum of the potentials due to individual charges.
  $$V = V_1 + V_2 + V_3 + \dots$$

---

4. Equipotential Surfaces

• A surface where the electric potential is constant at all points.
• Properties:
  • No work is done when moving a charge on an equipotential surface.
  • Equipotential surfaces are perpendicular to electric field lines.

---

5. Electrical Potential Energy

• The potential energy of a system of charges is the work done in assembling the charges.
• For Two-Point Charges: $$U = \frac{k q_1 q_2}{r}$$
• For an Electric Dipole in an External Field: $$U = - pE \cos\theta$$

---

6. Conductors and Insulators

• Conductors: Allow free movement of charges (e.g., metals).
• Insulators: Do not allow free charge movement (e.g., rubber, glass).

---

7. Free and Bound Charges

• Free Charges: Move freely inside a conductor.
• Bound Charges: Stay attached to atoms in insulators.

---

8. Dielectrics and Polarization

• Dielectric: An insulating material placed between capacitor plates.
• Polarization: Alignment of molecular dipoles in response to an electric field, reducing the effective field inside the material.

---

9. Capacitors and Capacitance

• Capacitor: A device used to store charge and energy.
• Capacitance (C): Ability of a capacitor to store charge. $$C = \frac{Q}{V}$$
  • Unit: Farad (F)

Parallel Plate Capacitor

• Without Dielectric: $$C = \frac{\varepsilon_0 A}{d}$$
• With Dielectric: $$C = \frac{K \varepsilon_0 A}{d}$$
  • $K$ = Dielectric constant

---

10. Combination of Capacitors

• Series Combination: $$\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \dots$$
• Parallel Combination: $$C_{\text{eq}} = C_1 + C_2 + C_3 + \dots$$

---

11. Energy Stored in a Capacitor

$$U = \frac{1}{2} C V^2$$ $$U = \frac{1}{2} Q V$$ $$U = \frac{Q^2}{2C}$$

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Chapter 4:

Moving Charges and Magnetism - Class 12 Physics (CBSE) Notes

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1. Magnetic Field

• A magnetic field is the region around a magnet or current-carrying conductor where a force is exerted on moving charges or other magnets.
• Symbol: $B$
• Unit: Tesla (T)
• Representation: Magnetic field lines show the direction of the field.

---

2. Oersted’s Experiment

• Hans Christian Oersted (1820) discovered that a current-carrying wire creates a magnetic field around it.
• Observation: A compass needle placed near a current-carrying wire deflects, showing that current produces a magnetic field.

---

3. Biot-Savart Law

• Gives the magnetic field due to a small current element.
• Formula: $$dB = \frac{\mu_0}{4\pi} \frac{I \, dl \, \sin\theta}{r^2}$$ where:
  • $dB$ = Small magnetic field
  • $I$ = Current
  • $dl$ = Small element of wire
  • $r$ = Distance from the element
  • $\theta$ = Angle between $dl$ and $r$
  • $\mu_0$ = Permeability of free space ($4\pi \times 10^{-7}$ Tm/A)

Application: Magnetic Field Due to a Circular Current Loop

• At the center of a circular loop of radius $R$: $$B = \frac{\mu_0 I}{2R}$$

---

4. Ampere’s Circuital Law

• Statement: The line integral of the magnetic field around a closed loop is proportional to the total current enclosed.
• Formula: $$\oint B \cdot dl = \mu_0 I_{\text{enc}}$$

Applications of Ampere’s Law

1. Magnetic Field Due to an Infinitely Long Straight Wire: $$B = \frac{\mu_0 I}{2\pi r}$$
2. Magnetic Field Inside a Long Straight Solenoid: $$B = \mu_0 n I$$ where $n = N/L$ (turns per unit length).

---

5. Force on a Moving Charge in Magnetic and Electric Fields

• Lorentz Force: The force on a charge due to electric and magnetic fields.
• Formula: $$F = q (E + v \times B)$$ where:
  • $q$ = Charge
  • $E$ = Electric field
  • $B$ = Magnetic field
  • $v$ = Velocity of charge

Special Cases:

• If $v$ is parallel to $B$, force = 0 (No deflection).
• If $v$ is perpendicular to $B$, the charge moves in a circular path.

---

6. Force on a Current-Carrying Conductor in a Magnetic Field

• Formula: $$F = B I L \sin\theta$$ where:
  • $I$ = Current
  • $L$ = Length of conductor
  • $\theta$ = Angle between $B$ and conductor

---

7. Force Between Two Parallel Current-Carrying Conductors

• Two parallel wires carrying current in the same direction attract.
• Two parallel wires carrying current in opposite directions repel.
• Formula: $$F = \frac{\mu_0 I_1 I_2}{2\pi d}$$ where $d$ is the separation between wires.

Definition of 1 Ampere

• If two parallel wires 1 meter apart carry equal currents and exert a force of $2 \times 10^{-7}$ N/m, then the current in each wire is 1 ampere.

---

8. Torque on a Current Loop in a Uniform Magnetic Field

• A current-carrying loop in a magnetic field experiences torque.
• Formula: $$\tau = B I A \sin\theta$$ where:
  • $A$ = Area of the loop
  • $\theta$ = Angle between normal to loop and $B$

---

9. Current Loop as a Magnetic Dipole

• A current-carrying loop behaves like a magnetic dipole with a magnetic dipole moment.
• Magnetic Dipole Moment: $$m = N I A$$ where $N$ is the number of turns.

---

10. Moving Coil Galvanometer

• A device used to detect small currents.

Sensitivity of a Galvanometer

• Current Sensitivity: $$S_i = \frac{\theta}{I} = \frac{N B A}{k}$$ where $k$ is the torsional constant.
• Increased by:
  • Increasing $N$ (number of turns)
  • Increasing $A$ (area)
  • Using a strong $B$ (magnetic field)

Conversion to Ammeter and Voltmeter

• To Ammeter: Connect a small resistance (shunt) in parallel.
• To Voltmeter: Connect a large resistance in series.
  

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Chapter 5:

Magnetism and Matter - Class 12 Physics (CBSE) Notes

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1. Bar Magnet

• A bar magnet is a rectangular piece of a magnetic material with north (N) and south (S) poles.
• Properties of a Bar Magnet:
  • Like poles repel, unlike poles attract.
  • Magnetic field inside the magnet is from S to N, and outside is from N to S.
  • A freely suspended magnet always aligns in the north-south direction.

---

2. Bar Magnet as an Equivalent Solenoid

• A bar magnet behaves like a solenoid (coil of wire carrying current).
• Similarity:
  • A current-carrying solenoid produces a magnetic field similar to a bar magnet.
  • The magnetic field inside a solenoid is uniform and strong.
  • Magnetic field lines outside the solenoid resemble those of a bar magnet.

---

3. Magnetic Field Due to a Magnetic Dipole (Bar Magnet)

• A magnetic dipole consists of two opposite magnetic poles separated by a small distance.

(a) Magnetic Field Along the Axis of a Bar Magnet (Axial Position)

• The magnetic field is stronger along the axis.

(b) Magnetic Field Perpendicular to the Axis (Equatorial Position)

• The magnetic field at this position is weaker than at the axial position.

---

4. Torque on a Magnetic Dipole in a Uniform Magnetic Field

• When a bar magnet (magnetic dipole) is placed in a uniform magnetic field, it experiences a torque.
• Effect of Torque:
  • The magnet tends to align with the magnetic field.
  • Greater torque is experienced when the magnet is perpendicular to the field.

---

5. Magnetic Field Lines

• Magnetic field lines show the direction of the magnetic field.
• Properties of Magnetic Field Lines:
  • They start from the north pole and end at the south pole (outside the magnet).
  • They never intersect.
  • More dense field lines indicate a stronger magnetic field.

---

6. Magnetic Properties of Materials

• Materials are classified based on their magnetic behavior:

Type	Properties	Examples
Diamagnetic	Weakly repelled by a magnet, no permanent dipole, induced magnetic moment opposite to applied field	Copper, Bismuth, Water, Gold
Paramagnetic	Weakly attracted, small permanent dipole moment, aligns slightly with an external field	Aluminum, Platinum, Oxygen
Ferromagnetic	Strongly attracted, forms permanent magnets, strongly aligns with an external field	Iron, Cobalt, Nickel

---

7. Magnetization of Materials

• Magnetization ($M$): The measure of how much a material gets magnetized when placed in a magnetic field.
• Formula: $$M = \frac{m}{V}$$ where:
  • $m$ = Magnetic moment
  • $V$ = Volume of the material

---

8. Effect of Temperature on Magnetic Properties

• Diamagnetic materials: Unaffected by temperature.
• Paramagnetic and ferromagnetic materials:
  • Increase in temperature → Decrease in magnetism.
  • Curie Temperature: The temperature above which a ferromagnetic material becomes paramagnetic.
    

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Chapter 6:

1. Electromagnetic Induction (EMI)

• Electromagnetic Induction is the process of generating an EMF (electromotive force) or current in a conductor when the magnetic flux linked with it changes.
• Discovered by Michael Faraday in 1831.

---

2. Faraday’s Laws of Electromagnetic Induction

First Law:

• Whenever magnetic flux linked with a coil changes, an EMF is induced in the coil.
• If the coil is closed, an induced current flows through it.

Second Law:

• The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux.
• Formula: $$e = - \frac{d\phi}{dt}$$ where:
  • $e$ = Induced EMF
  • $\phi$ = Magnetic flux ($\phi = B A \cos\theta$)
  • $B$ = Magnetic field
  • $A$ = Area of the coil
  • $\theta$ = Angle between $B$ and normal to the coil

---

3. Lenz’s Law

• Statement: The induced current always flows in such a direction that it opposes the change in magnetic flux producing it.
• Formula: $$e = - \frac{d\phi}{dt}$$ The negative sign shows the opposing nature of the induced EMF.

Example of Lenz’s Law:

• When a magnet is moved towards a coil, the induced current opposes the approaching magnet.

---

4. Self and Mutual Induction

(a) Self Induction

• When the current in a coil changes, the flux linked with the same coil changes, inducing an EMF in the coil itself.
• Formula: $$e = - L \frac{dI}{dt}$$ where:
  • $L$ = Self-inductance (Henry, H)
  • $dI/dt$ = Rate of change of current

(b) Mutual Induction

• When current in one coil changes, it induces an EMF in a nearby coil.
• Formula: $$e = - M \frac{dI}{dt}$$ where:
  • $M$ = Mutual inductance (Henry, H)

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Alternating Current - Class 12 Physics (CBSE) Notes

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1. Alternating Current (AC)

• Alternating current (AC) is a current that changes direction periodically.

• AC Voltage Equation:

  $$V = V_0 \sin(\omega t)$$

  where:

  • $V_0$ = Peak voltage
  • $\omega$ = Angular frequency
  • $t$ = Time

• Frequency of AC in India = 50 Hz

---

2. Peak and RMS Value of AC

Peak Value ($I_0$ or $V_0$)

• The maximum value of AC current or voltage.

Root Mean Square (RMS) Value

• The effective value of AC, which produces the same heating effect as DC.
• Formula: $$I_{\text{rms}} = \frac{I_0}{\sqrt{2}}, \quad V_{\text{rms}} = \frac{V_0}{\sqrt{2}}$$

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Chapter 8:

1. Displacement Current

• Displacement current ($I_D$) is the current produced in a capacitor due to a changing electric field.
• Introduced by James Clerk Maxwell to explain how a changing electric field produces a magnetic field.
• Formula: $$I_D = \epsilon_0 \frac{d\phi_E}{dt}$$ where:
  • $\epsilon_0$ = Permittivity of free space
  • $\phi_E$ = Electric flux

---

2. Electromagnetic Waves (EM Waves)

• Electromagnetic waves are waves that consist of oscillating electric and magnetic fields perpendicular to each other and perpendicular to the direction of propagation.
• They do not require a medium and can travel in a vacuum.
• Speed of EM waves in a vacuum: $$c = 3 \times 10^8 \text{ m/s}$$

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3. Characteristics of Electromagnetic Waves

• Transverse in nature: Electric and magnetic fields are perpendicular to each other and the direction of wave propagation.
• Travel with the speed of light in vacuum ($c = 3 \times 10^8$ m/s).
• Carry energy and momentum.
• Can be polarized.

---

4. Electromagnetic Spectrum

The electromagnetic spectrum consists of different types of EM waves arranged according to their frequency and wavelength.

Type of Wave	Wavelength Range	Uses
Radio Waves	$> 1$ m	Communication (TV, Radio, Mobile networks)
Microwaves	$10^{-3}$ m – 1 m	Cooking (Microwave ovens), Radar, GPS
Infrared (IR)	$10^{-6}$ m – $10^{-3}$ m	Remote controls, Night vision, Heating
Visible Light	$4 \times 10^{-7}$ m – $7 \times 10^{-7}$ m	Human vision, Optical fiber communication
Ultraviolet (UV)	$10^{-8}$ m – $4 \times 10^{-7}$ m	Sterilization, Vitamin D production
X-rays	$10^{-12}$ m – $10^{-8}$ m	Medical imaging (X-rays), Security scanning
Gamma Rays	$< 10^{-12}$ m	Cancer treatment, Nuclear reactions

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Chapter 9:

1. Reflection of Light

• Reflection: Bouncing back of light from a smooth surface.
• Laws of Reflection:
  1. The incident ray, reflected ray, and normal lie in the same plane.
  2. The angle of incidence ($i$) = The angle of reflection ($r$).

---

2. Spherical Mirrors

• Concave Mirror: Converging mirror (forms real/inverted or virtual/upright images).
• Convex Mirror: Diverging mirror (forms only virtual, upright, and diminished images).

Mirror Formula

$$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$

where:

• $f$ = Focal length
• $u$ = Object distance
• $v$ = Image distance

Magnification ($m$):

$$m = \frac{-v}{u}$$

• $m > 1$ → Enlarged image
• $m < 1$ → Diminished image
• $m$ positive → Virtual image
• $m$ negative → Real image

---

3. Refraction of Light

• Refraction: Bending of light as it passes from one medium to another.
• Laws of Refraction:
  1. The incident ray, refracted ray, and normal lie in the same plane.
  2. Snell’s Law: $$n_1 \sin i = n_2 \sin r$$ where $n_1$ and $n_2$ are refractive indices of the two media.

---

4. Total Internal Reflection (TIR) & Optical Fibers

• Total Internal Reflection occurs when:
  1. Light moves from denser to rarer medium.
  2. Angle of incidence exceeds the critical angle ($C$).

Applications of TIR:

• Optical fibers (used in communication, endoscopy).
• Mirage (illusion of water in deserts).
• Diamond’s brilliance (due to high refractive index).

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5. Refraction at Spherical Surfaces & Lenses

• Thin Lens Formula: $$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$
• Lens Maker’s Formula: $$\frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$$ where:
  • $n$ = Refractive index of lens material
  • $R_1, R_2$ = Radii of curvature of lens surfaces

Magnification by a Lens:

$$m = \frac{h'}{h} = \frac{v}{u}$$

Power of a Lens:

$$P = \frac{100}{f} \quad (\text{in diopters, D})$$

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6. Combination of Thin Lenses in Contact

• Formula for Equivalent Focal Length: $$\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} + \frac{1}{f_3} + \dots$$
• Power of Combined Lenses: $$P = P_1 + P_2 + P_3 + \dots$$

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7. Refraction Through a Prism

• Deviation Angle ($\delta$): Angle between incident and emergent rays.
• Formula: $$\delta = i + e - A$$ where:
  • $i$ = Angle of incidence
  • $e$ = Angle of emergence
  • $A$ = Angle of prism

Minimum Deviation Condition:

$$n = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin(A/2)}$$

where $D_m$ = Minimum deviation angle.

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8. Optical Instruments

(a) Microscope

• Simple Microscope (Magnifying Glass):

  • Magnification: $M = 1 + \frac{D}{f}$, where $D$ = Near point (25 cm).

• Compound Microscope:

  • Magnification: $M = m_o \times m_e$, where:
    • $m_o = \frac{v_o}{u_o}$ (Objective magnification).
    • $m_e = 1 + \frac{D}{f_e}$ (Eyepiece magnification).

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(b) Telescope

• Refracting Telescope:

  • Magnification: $$M = \frac{f_o}{f_e}$$ where $f_o$ = Focal length of objective lens, $f_e$ = Focal length of eyepiece.

• Reflecting Telescope (Uses concave mirror instead of lens for objective).

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  Chapter 10:

  1. Wave Front and Huygen’s Principle

• Wavefront: A continuous locus of points vibrating in the same phase.
• Huygen’s Principle:
  1. Every point on a wavefront acts as a secondary wave source.
  2. The new wavefront is the tangent to these secondary waves.

Types of Wavefronts

• Spherical (Point source)
• Plane (Distant source)
• Cylindrical (Line source)

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2. Reflection and Refraction Using Wavefronts

• Reflection: Angle of incidence ($i$) = Angle of reflection ($r$) (verified using wavefronts).
• Refraction: Huygen’s principle gives Snell’s Law: $$\frac{\sin i}{\sin r} = \frac{v_1}{v_2} = n_{21}$$ where $v_1$ and $v_2$ are the speeds of light in different media.

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3. Interference of Light

• Interference: Superposition of two coherent waves to form a pattern of alternating bright and dark fringes.
• Coherent Sources: Two sources having the same frequency and constant phase difference.

Young’s Double Slit Experiment (YDSE)

• Fringe Width ($\beta$): $$\beta = \frac{\lambda D}{d}$$ where:
  • $\lambda$ = Wavelength of light
  • $D$ = Distance between screen and slits
  • $d$ = Distance between the two slits

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4. Diffraction of Light (Single Slit)

• Diffraction: Bending of light around the edges of an obstacle.
• Width of Central Maxima: $$w = \frac{2\lambda D}{a}$$ where:
  • $a$ = Slit width
  • $D$ = Distance to the screen

•  
  

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Chapter 11:

1. Dual Nature of Radiation

• Dual Nature: Radiation exhibits both wave and particle nature.
  • Wave Nature: Explains interference, diffraction, and polarization.
  • Particle Nature: Explains phenomena like the photoelectric effect.

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2. Photoelectric Effect

• Photoelectric Effect: Emission of electrons from a metal surface when light of a certain frequency (threshold frequency) shines on it.
• Hertz and Lenard’s Observations:
  1. Electrons are emitted immediately when light hits the metal surface.
  2. The number of electrons emitted depends on the intensity of light, not its frequency.
  3. No electrons are emitted if the frequency of light is below the threshold frequency, regardless of intensity.

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3. Einstein’s Photoelectric Equation

• Einstein's Photoelectric Equation:

  $$E_k = h\nu - \phi$$

  where:

  • $E_k$ = Kinetic energy of the emitted electron
  • $h$ = Planck's constant
  • $\nu$ = Frequency of the incident light
  • $\phi$ = Work function (minimum energy required to emit an electron from the metal)

• Particle Nature of Light: Light behaves as photons (particles) carrying energy $E = h\nu$.

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4. Experimental Study of Photoelectric Effect

• Observation:
  • Current vs Voltage Graph: A graph of current (number of emitted electrons) vs stopping potential (to stop the emitted electrons) shows a linear relation.
  • Effect of Intensity: Increasing the intensity of light increases the number of emitted electrons, but the energy of electrons remains the same.
  • Effect of Frequency: Increasing the frequency of light increases the energy of the emitted electrons, provided the frequency is above the threshold frequency.

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5. Matter Waves

• Wave Nature of Particles: Particles like electrons also exhibit wave properties (de Broglie hypothesis).

  • de-Broglie Wavelength: $$\lambda = \frac{h}{p}$$ where:
    • $\lambda$ = Wavelength
    • $h$ = Planck’s constant
    • $p$ = Momentum of the particle

• Matter Waves: Particles such as electrons have associated wave-like behavior, which is observed in phenomena like electron diffraction.

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  Chapter 12:

  1. Alpha-Particle Scattering Experiment

• Experiment: Conducted by Rutherford to probe the structure of the atom.
  • Observation: Most alpha particles passed through gold foil, but some were deflected at large angles, and a few were reflected.
  • Conclusion: The atom has a small, dense nucleus at the center, with electrons revolving around it.

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2. Rutherford's Model of the Atom

• Model: The atom consists of a small, dense nucleus containing positive charge (protons) at the center. Electrons revolve around the nucleus in circular orbits.

• Key Points:

  1. The mass of the atom is concentrated in the nucleus.
  2. Electrons move in orbits due to electrostatic attraction with the nucleus.
  3. The atom is mostly empty space.

• Limitations:

  • It could not explain the stability of the atom or the spectrum of hydrogen.

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3. Bohr's Model of the Hydrogen Atom

• Bohr's Postulates:
  1. Electrons revolve in fixed, stable orbits without radiating energy.
  2. An electron can only gain or lose energy when it jumps from one orbit to another, emitting or absorbing a photon.
  3. The angular momentum of an electron in a stable orbit is quantized: $$L = n\hbar \quad (n = 1, 2, 3, \dots)$$ where $\hbar$ = reduced Planck’s constant ($\hbar = \frac{h}{2\pi}$).

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4. Expression for Radius of nth Orbit

• Radius of nth orbit in the Bohr model: $$r_n = \frac{n^2 h^2}{4 \pi^2 m_e e^2 Z}$$ where:
  • $r_n$ = radius of nth orbit
  • $n$ = Principal quantum number
  • $m_e$ = Mass of the electron
  • $e$ = Charge of the electron
  • $Z$ = Atomic number (1 for hydrogen)

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5. Velocity and Energy of Electron in nth Orbit

• Velocity of electron in nth orbit:

  $$v_n = \frac{2 \pi k e^2}{h n}$$

  where:

  • $k$ = Coulomb's constant
  • $h$ = Planck’s constant
  • $e$ = Electron charge

• Energy of electron in nth orbit:

  $$E_n = - \frac{13.6}{n^2} \, \text{eV}$$
  • The negative sign indicates that the energy is lower than the energy of an unbound electron (which is taken as zero).
  • Energy is quantized.

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6. Hydrogen Line Spectra (Qualitative Treatment)

• Hydrogen Spectrum: The emission spectrum of hydrogen consists of discrete lines (not a continuous spectrum) due to electron transitions between different orbits.
  • Lyman series: Transitions to $n = 1$ (ultraviolet region).
  • Balmer series: Transitions to $n = 2$ (visible region).
  • Paschen series: Transitions to $n = 3$ (infrared region).

     

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Chapter 13:

1. Composition and Size of Nucleus

• Composition of Nucleus:

  • Nucleus consists of protons (positively charged) and neutrons (neutral) collectively known as nucleons.
  • The number of protons determines the atomic number ($Z$), while the total number of nucleons (protons + neutrons) determines the mass number ($A$).

• Size of Nucleus:

  • The radius of a nucleus is given by the formula: $$R = R_0 A^{1/3}$$ where:
    • $R_0$ = constant $\approx 1.2 \, \text{fm}$
    • $A$ = mass number of the nucleus
    • $R$ = radius of the nucleus

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2. Nuclear Force

• Nuclear Force:
  • The force between nucleons (protons and neutrons) in the nucleus is called the nuclear force.
  • It is a strong force and is attractive in nature, operating at very short distances (on the order of femtometers).
  • Unlike the electrostatic force, the nuclear force does not depend on the charge and is independent of the type of nucleon (proton or neutron).

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3. Mass-Energy Relation

• Einstein’s Mass-Energy Equivalence:

  • The energy ($E$) of a body is related to its mass ($m$) by the equation: $$E = mc^2$$ where:
    • $E$ = Energy
    • $m$ = Mass
    • $c$ = Speed of light ($3 \times 10^8 \, \text{m/s}$)

• Mass Defect:

  • The difference between the sum of the masses of individual nucleons and the mass of the nucleus is called the mass defect.
  • The mass defect is converted into binding energy, which holds the nucleus together.

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4. Binding Energy

• Binding Energy:

  • The binding energy of a nucleus is the energy required to break it into its individual nucleons.
  • It is given by: $$E_b = \Delta m \, c^2$$ where:
    • $E_b$ = Binding energy
    • $\Delta m$ = Mass defect
    • $c$ = Speed of light

• Binding Energy per Nucleon:

  • The binding energy per nucleon is the total binding energy divided by the number of nucleons.
  • The average binding energy per nucleon increases with mass number up to iron ($A \approx 56$) and then decreases for heavier nuclei.

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5. Nuclear Fission

• Nuclear Fission:
  • The process of splitting a heavy nucleus (such as uranium-235) into two smaller nuclei along with the release of a large amount of energy.
  • Fission typically occurs when a nucleus absorbs a neutron, becomes unstable, and splits.
  • Fission is the principle behind nuclear reactors and atomic bombs.

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6. Nuclear Fusion

• Nuclear Fusion:
  • The process of combining two light nuclei (such as hydrogen) to form a heavier nucleus, releasing a large amount of energy.
  • Fusion powers stars, including the Sun, where hydrogen nuclei fuse to form helium, releasing energy in the form of light and heat.
    

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Chapter 14:

 

1. Energy Bands in Conductors, Semiconductors, and Insulators

• Energy Bands:
  • Conductors: In conductors (e.g., metals), the valence band and conduction band overlap, allowing electrons to flow freely, which makes them good conductors of electricity.
  • Semiconductors: In semiconductors (e.g., silicon), the valence band is filled, and the conduction band is empty, with a small energy gap (called band gap) between them. At room temperature, some electrons move to the conduction band, making them conduct electricity.
  • Insulators: In insulators, the band gap between the valence band and conduction band is large, preventing electrons from moving to the conduction band, making them poor conductors of electricity.

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2. Intrinsic and Extrinsic Semiconductors

Intrinsic Semiconductors

• Intrinsic Semiconductor: Pure semiconductors (e.g., silicon, germanium) without any impurities.
• In intrinsic semiconductors, the number of free electrons equals the number of holes (positive charge carriers).
• The electrical conductivity of intrinsic semiconductors is relatively low.

Extrinsic Semiconductors

• Extrinsic Semiconductor: A semiconductor that is doped with impurities to improve its electrical conductivity.
  • p-type Semiconductor: Doped with acceptor impurities (e.g., boron in silicon) that create holes (positive charge carriers).
  • n-type Semiconductor: Doped with donor impurities (e.g., phosphorus in silicon) that add free electrons (negative charge carriers).

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3. P-N Junction

• P-N Junction: The junction formed between a p-type and an n-type semiconductor.
  • At the junction, free electrons from the n-type region combine with holes from the p-type region, creating a depletion region with no charge carriers, and forming a potential barrier.

Working of P-N Junction

• Forward Bias: When the positive terminal of the battery is connected to the p-type and the negative terminal to the n-type, the potential barrier is reduced, and current flows through the junction.
• Reverse Bias: When the positive terminal is connected to the n-type and the negative terminal to the p-type, the potential barrier increases, preventing current from flowing.

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4. Semiconductor Diode - I-V Characteristics

• I-V Characteristics of a diode show the relationship between the current (I) flowing through the diode and the voltage (V) across it.
  • Forward Bias: The current increases rapidly after a small threshold voltage (typically around 0.7V for silicon diodes).
  • Reverse Bias: No current flows until a very high reverse voltage is applied (breakdown region), beyond which the diode may be damaged.

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5. Application of Junction Diode - Diode as a Rectifier

• Rectification: The process of converting alternating current (AC) into direct current (DC).
  • Half-Wave Rectifier: Only one half of the AC waveform is allowed to pass through the diode. The output is a pulsating DC.
  • Full-Wave Rectifier: Both halves of the AC waveform are used, providing a smoother DC output.
  • In both cases, the diode only allows current to pass in one direction, acting as a rectifier.