Magnetism, Electromagnetic Induction and Alternating Current — NEET Physics

Electricity and magnetism are two faces of one force. A moving charge feels a magnetic force; a changing magnetic field drives a current. This chapter runs the full arc — the magnetic force on charges and currents, the fields that currents create, then electromagnetic induction (how changing flux generates EMF) and finally alternating current (rms values, reactance, resonance, transformers). Together these are a reliable 4–5 NEET marks and the physics behind every motor, generator and power grid.

Part A — Magnetism

1. Magnetic force on a moving charge

A charge moving through a magnetic field feels a force perpendicular to both its velocity and the field:

$F=qvB\sin \theta$

• Maximum when $v\perp B$ ($\theta =90°$); zero when the charge moves parallel to the field ($\theta =0$).
• The force is always perpendicular to $v$, so it does no work — it changes direction, not speed.
• Direction from Fleming's left-hand rule (or $\vec{F}=q\vec{v}\times \vec{B}$).

2. Force on a current-carrying conductor

A current is moving charge, so a wire in a field feels:

$F=BIL\sin \theta$

• A 1 m wire carrying 2 A across a 0.5 T field ($\theta =90°$): $F=0.5\times 2\times 1=1$ N.
• Zero force when the current is parallel to the field. This force runs every electric motor.

3. Fields created by currents

with ${\mu }_0=4\pi \times 10^{-7}$ T·m/A. Direction from the right-hand grip rule.

4. Circular motion of a charge in a field

Since the magnetic force is always perpendicular to velocity, a charge entering a uniform field perpendicular moves in a circle:

$qvB=\frac{m{v}^2}{r}\Rightarrow r=\frac{mv}{qB}$

• The radius grows with momentum and shrinks with field or charge. This is the basis of the cyclotron and mass spectrometer.

Part B — Electromagnetic Induction

5. Magnetic flux, Faraday's and Lenz's laws

Flux is the field threading a loop: $\Phi =BA\cos \theta$. A changing flux induces an EMF:

$\epsilon =-\frac{d\Phi }{dt}$

• Faraday's law: the induced EMF equals the rate of change of flux.
• Lenz's law (the minus sign): the induced current opposes the change that created it — a consequence of energy conservation. Push a magnet into a coil and the coil pushes back.

6. Motional EMF

A rod of length $L$ moving at speed $v$ perpendicular to a field $B$ generates:

$\epsilon =BLv$

• $B=0.5$ T, $L=1$ m, $v=2$ m/s: $\epsilon =0.5\times 1\times 2=1$ V. This is how a generator converts motion into voltage.

7. Inductance

• Self-inductance $L$: a changing current in a coil induces an EMF in itself, $\epsilon =-L\frac{dI}{dt}$.
• Energy stored in an inductor: $E=\frac{1}{2}L{I}^2$ (analogue of $\frac{1}{2}C{V}^2$ for a capacitor).
• Mutual inductance couples two coils — the principle of the transformer.

Part C — Alternating Current

8. RMS values

AC voltage and current vary sinusoidally; the rms value is the effective (heating-equivalent) value:

$I_{\text{rms}}=\frac{I_0}{\sqrt{2}},V_{\text{rms}}=\frac{V_0}{\sqrt{2}}$

• Peak current 10 A → $I_{\text{rms}}=10/\sqrt{2}\approx 7.07$ A.
• Indian mains "220 V" is the rms; its peak is $220\sqrt{2}\approx 311$ V.

9. Reactance, impedance and resonance

• Inductive reactance $X_L=\omega L=2\pi fL$ (grows with frequency).
• Capacitive reactance $X_C=\frac{1}{\omega C}$ (falls with frequency).
• Impedance $Z=\sqrt{R^2+(X_L-X_C{)}^2}$; current $I_{\text{rms}}=V_{\text{rms}}/Z$.
• Resonance ($X_L=X_C$) gives minimum impedance and maximum current at:

$f_0=\frac{1}{2\pi \sqrt{LC}}$

Worked example 9.1. At 50 Hz, an inductor $L=0.1$ H has $X_L=2\pi \times 50\times 0.1=31.4$ Ω.

At resonance the circuit is purely resistive — the tuning principle of radios.

10. The transformer

A transformer changes AC voltage by mutual induction, conserving power (ideally):

$\frac{V_s}{V_p}=\frac{N_s}{N_p},V_p{I}_p=V_s{I}_s$

• A step-up transformer with $N_p=100$, $N_s=1000$ turns raises 220 V to $V_s=220\times \frac{1000}{100}=2200$ V.
• Step-up transformers raise voltage (and cut current) for efficient long-distance transmission; step-down transformers reverse it near homes.

11. Common traps NEET sets here

• Magnetic force does work — false; it is always perpendicular to $v$, so it changes only direction.
• Force on a charge moving parallel to $B$ — it is zero, not maximum.
• Forgetting Lenz's minus sign — the induced current always opposes the change.
• Peak vs rms — mains "220 V" is rms; the peak is 311 V.
• $X_L$ and $X_C$ frequency behaviour — $X_L$ rises, $X_C$ falls with frequency; they are equal at resonance.
• Transformers on DC — they need changing flux, so they don't work on steady DC.

12. Memory aids

• "Magnetic force never works" — always perpendicular to velocity.
• "BIL sin θ, BLv" — force on a wire; motional EMF.
• "Lenz opposes" — the induced effect fights the change.
• "rms = peak over root-2" — 220 V rms ↔ 311 V peak.
• "XL up, XC down, equal at resonance" — reactance with frequency.

13. Exam protocol

1. Magnetic force $F=qvB\sin \theta$ (charge) and $BIL\sin \theta$ (wire); zero when parallel, and it does no work.
2. Circular radius in a field $r=mv/qB$.
3. Field of a wire ${\mu }_{0}I/2\pi r$, loop ${\mu }_{0}I/2R$, solenoid ${\mu }_{0}nI$.
4. Induced EMF $=-d\Phi /dt$ (Faraday); direction opposes change (Lenz); motional EMF $BLv$.
5. Inductor energy $\frac{1}{2}L{I}^2$.
6. AC: $I_{\text{rms}}=I_0/\sqrt{2}$; $X_L=\omega L$, $X_C=1/\omega C$; resonance $f_0=1/2\pi \sqrt{LC}$.
7. Transformer $V_s/V_p=N_s/N_p$ — AC only.