Lesson Overview

Unit 8 explains magnetic fields, force on current-carrying conductors, Ampere’s law, electromagnetic induction, Faraday’s and Lenz’s laws, alternating current (AC), transformers, generators, motors, and inductive/reactive components. This is one of the most important units for understanding electrical machines and power systems.

1. Core Concepts (Short Notes)

8.1 Magnetic Field & Magnetic Force

• Magnetic field (B): Region where moving charges or magnets experience force.

• Unit: tesla (T).

• Force on a current-carrying conductor:F = B I L sinθ.

• Force on a moving charge:F = q v B sinθ.

8.2 Ampere’s Law

• Magnetic field around a long straight conductor:B = μ₀I / (2πr).

• Inside solenoid:B = μ₀nI (n = turns per meter).

8.3 Electromagnetic Induction

• Induced emf when flux changes.

• Faraday’s Law:ε = − dΦ/dt.

• Lenz’s Law: Direction opposes change.

8.4 Alternating Current (AC)

• AC voltage: V = V₀ sin(ωt).

• RMS values:Vᵣₘₛ = V₀ / √2;Iᵣₘₛ = I₀ / √2.

8.5 Inductive & Capacitive Reactance

• Inductive reactance:X_L = ωL.

• Capacitive reactance:X_C = 1/(ωC).

• Impedance:Z = √(R² + (X_L − X_C)²).

8.6 Transformers

• Step-up/down.

• Turns ratio:V_s / V_p = N_s / N_p.

• Efficiency:η = (P_out / P_in) × 100%.

8.7 Generators & Motors

• AC generator: electromagnetic induction.

• DC motor: force on coil in magnetic field.

2. Detailed Notes for Each Section

8.1 Magnetic Field & Forces

Magnetic Force on a Conductor

F = BIL sinθ.

Fleming’s Left-Hand Rule

• Thumb → Force

• First finger → Field

• Second finger → Current

Force on Moving Charge

F = qvB sinθ.

• Direction given by right-hand rule.

8.2 Magnetic Fields of Conductors & Solenoids

Long Straight Conductor

B = μ₀I / (2πr).Circular field lines around wire.

Solenoid

B = μ₀nI.

• Almost uniform field inside.

• Direction: right-hand grip rule.

8.3 Electromagnetic Induction

Magnetic Flux

Φ = BA cosθ.

Faraday’s Law

ε = − dΦ/dt.

• Negative sign from Lenz’s law.

Lenz’s Law

• Induced emf opposes the cause producing it.

• Conserves energy.

Applications

• AC generator

• Transformers

• Induction cookers

• Speedometers

8.4 Alternating Current (AC)

Instantaneous Values

V = V₀ sinωt.I = I₀ sinωt.

RMS Values

Vᵣₘₛ = V₀ / √2.Iᵣₘₛ = I₀ / √2.

Power in AC Circuits

P = Vᵣₘₛ Iᵣₘₛ cosφ (power factor).

8.5 Inductive & Capacitive Reactance

Inductor

X_L = ωL.Current lags by 90°.

Capacitor

X_C = 1/(ωC).Current leads by 90°.

Impedance of RLC Circuit

Z = √(R² + (X_L - X_C)²).

Resonance

Occurs when X_L = X_C.Frequency:ω₀ = 1/√(LC).

8.6 Transformers

Ideal Transformer Equations

Energy Losses

• Eddy currents

• Hysteresis

• Copper losses

• Flux leaks

Increasing Efficiency

• Laminated cores

• Soft iron cores

• Good winding materials

8.7 Generators & Motors

AC Generator

Induced emf produced due to rotating coil in magnetic field.ε = ε₀ sinωt.

DC Motor

• Current in coil experiences force → rotation.

• Uses commutator.

Fleming’s Rules

• Generator: Right-hand rule.

• Motor: Left-hand rule.

3. Formula Summary (Unit 8)

• F = BIL sinθ

• F = qvB sinθ

• B = μ₀I / (2πr)

• B(solenoid) = μ₀nI

• Φ = BA cosθ

• ε = −dΦ/dt

• V = V₀ sinωt

• Vᵣₘₛ = V₀ / √2

• X_L = ωL

• X_C = 1/(ωC)

• Z = √(R² + (X_L - X_C)²)

• V_s/V_p = N_s/N_p

4. Common Mistakes to Avoid

• Confusing left-hand and right-hand rules.

• Forgetting phase differences in AC circuits.

• Not applying Lenz’s law for induced current direction.

• Using RMS instead of peak values incorrectly.

• Forgetting core losses in transformer problems.

5. Exam Tips

• Draw clear diagrams for fields and circuits.

• Label directions using hand rules.

• Check units (henry, farad, ohm, tesla).

• Use phasor diagrams where needed.

• In transformer questions, always state “assuming ideal transformer unless losses considered.”

6. Quick Revision Table