Physics

🚀 CBSE Class 12 Physics – First 5 Chapters

Interactive Guide: All Important Formulas + Concepts + Many Practice Questions

1. Electric Charges and Fields

Core Concepts: Coulomb’s law, Electric field, Gauss’s law, Electric field lines.

Important Formulas:
Coulomb’s Law: \( F = \frac{1}{4\pi\epsilon_0} \frac{|q_1 q_2|}{r^2} = k \frac{|q_1 q_2|}{r^2} \) (k = 9 × 10⁹)
Electric Field: \( \vec{E} = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2} \hat{r} \)
Gauss’s Theorem: \( \oint \vec{E} \cdot d\vec{A} = \frac{q_{encl}}{\epsilon_0} \)
Infinite line charge: \( E = \frac{\lambda}{2\pi\epsilon_0 r} \)
Infinite sheet: \( E = \frac{\sigma}{2\epsilon_0} \)

Quick Think 1: Why is electric field inside a conductor zero?
Answer: Charges reside on surface only. Any Gaussian surface inside encloses zero charge.

Quick Think 2: Field lines never cross. Why?
Answer: At crossing point, electric field would have two directions simultaneously — impossible.

2. Electrostatic Potential and Capacitance

Core Concepts: Potential, Equipotential surfaces, Capacitance, Energy stored.

Important Formulas:
Potential due to point charge: \( V = \frac{1}{4\pi\epsilon_0} \frac{q}{r} \)
Potential energy of two charges: \( U = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r} \)
Capacitance: \( C = \frac{Q}{V} \)
Parallel plate capacitor: \( C = \frac{\epsilon_0 A}{d} \)
Energy stored: \( U = \frac{1}{2} C V^2 = \frac{Q^2}{2C} = \frac{1}{2} Q V \)
Series: \( \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} \)
Parallel: \( C_{eq} = C_1 + C_2 \)

Quick Think: Why is potential constant inside a charged conductor?
Answer: E = 0 inside, so work done to move charge is zero → ΔV = 0.

3. Current Electricity

Core Concepts: Ohm’s law, Kirchhoff’s laws, Wheatstone bridge, Cells.

Important Formulas:
Current: \( I = ne A v_d \)
Ohm’s law: \( V = IR \)
Resistance: \( R = \rho \frac{l}{A} \)
Temperature dependence: \( R = R_0 (1 + \alpha \Delta T) \)
Series resistance: \( R_{eq} = R_1 + R_2 \)
Parallel: \( \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \)

Quick Think: A wire of resistance 4Ω is stretched to double its length. New resistance?
Answer: 16Ω (length doubles, area halves → R becomes 4 times).

4. Moving Charges and Magnetism

Core Concepts: Biot-Savart law, Ampere’s law, Lorentz force, Cyclotron.

Important Formulas:
Biot-Savart law: \( d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \hat{r}}{r^2} \)
Straight wire: \( B = \frac{\mu_0 I}{2\pi r} \)
Lorentz force: \( \vec{F} = q (\vec{v} \times \vec{B}) \)
Force on wire: \( \vec{F} = I (\vec{l} \times \vec{B}) \)
Cyclotron frequency: \( f = \frac{qB}{2\pi m} \)

5. Magnetism and Matter

Core Concepts: Bar magnet, Magnetic materials (Dia/Para/Ferro), Hysteresis, Curie’s law.

Important Formulas:
Magnetic field due to bar magnet (axial): \( B = \frac{\mu_0}{4\pi} \frac{2M}{d^3} \)
Equatorial: \( B = \frac{\mu_0}{4\pi} \frac{M}{d^3} \)
\( B = \mu_0 (H + M) \)
Susceptibility: \( \chi_m = \frac{M}{H} \), \( \mu_r = 1 + \chi_m \)

Board Tips

Revise all derivations (Gauss’s law, torque on dipole, energy in capacitor). Draw neat labelled diagrams. Practice numericals daily.