Electricity & Magnetism — Part 1: 40 MCQs with Explanations

Lenz's law states that induced current flows in a direction that opposes the change causing it.

1/R_eq = 1/4 + 1/6 = 5/12, so R_eq = 12/5 = 2.4 Ω.

Transformer works on mutual induction between primary and secondary coils.

Power factor = cosφ, where φ is phase angle between voltage and current. For pure resistance, φ = 0, so cos0 = 1.

Energy U = ½CV² = ½QV = Q²/2C.

B = μ₀I/2R at center of circular loop.

I_rms = I₀/√2 for sinusoidal AC.

In pure capacitor, current leads voltage by 90° (π/2 radians).

Diamagnetic materials have small negative susceptibility (χ < 0).

Time constant τ = RC for charging/discharging of capacitor through resistor.

E = σ/2ε₀ (independent of distance from sheet).

Balance condition: P/Q = R/S (ratio of resistances in opposite arms equal).

C = Kε₀A/d = K times capacitance without dielectric (C₀ = ε₀A/d).

Angle of dip (inclination) is 90° at magnetic poles where field lines are vertical.

Magnetic dipole moment m = IA has units Ampere-meter² (Am²).

V = q/4πε₀r (scalar quantity).

Resistance R = ρL/A, where ρ is resistivity (depends on material), L is length, and A is cross-sectional area. Therefore, resistance depends on all three factors.

Energy stored U = ½QV = ½(CV)V = ½CV², where Q = CV is the charge on the capacitor.

Inside a long solenoid, the magnetic field is uniform, parallel to the axis of the solenoid, and has magnitude B = μ₀nI, where n is number of turns per unit length and I is current.

Ohm's law states that for a conductor at constant temperature, current (I) is directly proportional to potential difference (V): V ∝ I or V = IR.

Electric field E = kQ/r², so E ∝ Q (for fixed distance r).

Electric potential V = kQ/r, so V ∝ Q and V ∝ 1/r.

Power P = VI = (IR)I = I²R (using Ohm's law V = IR).

Capacitance C = ε₀KA/d, where K is dielectric constant. Inserting a dielectric (K > 1) increases capacitance. Decreasing area or increasing separation decreases capacitance.

For series combination: 1/C = 1/C₁ + 1/C₂ = 1/6 + 1/6 = 2/6 = 1/3. Therefore, C = 3 μF.

Diamagnetic substances have small negative susceptibility (χ ≈ -10⁻⁵), independent of temperature. They are weakly repelled by magnetic fields.

In electrostatic conditions, electric field inside a conductor is zero. All excess charge resides on the outer surface.

Power factor = cosφ = R/Z, where R is resistance and Z is impedance. For RL circuit, 0 < cosφ < 1 (lagging).

Gauss's law: Φ = Q/ε₀, where Q is net charge enclosed by the Gaussian surface.

Magnetic moment μ = IA, with direction given by right-hand rule (perpendicular to plane of loop).

For infinite sheet with uniform surface charge density σ: E = σ/2ε₀, constant at all distances from the sheet.

Electric dipole moment p = qd, direction from negative to positive charge.

Energy in capacitor is stored in the electric field between the plates: U = ½ε₀E² × volume.

Faraday's law: ε = -ΔΦ/Δt = -(0.1-0.5)/0.2 = -(-0.4)/0.2 = 2.0 V.

Charge of electron e = 1.6 × 10⁻¹⁹ C. Number of electrons n = Q/e = 1/(1.6 × 10⁻¹⁹) = 6.25 × 10¹⁸.

Diamagnetic materials have small negative susceptibility (χ < 0, typically ~ -10^-5). Paramagnetic: small positive; ferromagnetic: large positive.

Time constant τ = RC for charging/discharging of capacitor through resistor. After τ, capacitor charges to ~63% of max voltage.

Balance condition: P/Q = R/S (ratio of resistances in opposite arms equal). No current flows through galvanometer at balance.

Angle of dip (inclination) is 90° at magnetic poles where field lines are vertical; 0° at magnetic equator where field lines are horizontal.

Magnetic dipole moment m = IA has units Ampere-meter² (Am²).