Electromagnetic Induction and AC formulas for JEE Main & Advanced

23 formula entries for Electromagnetic Induction and AC, in the order the chapter builds them. Each shows the formula, when to use it and the first trap to avoid.

Magnetic Flux

Φ_{B} = \int \vec{B} \cdot d \vec{A} = B A \cos θ

When to use. Use to quantify magnetic field linkage in Faraday's law or to compute induced EMF.

Trap. Forgetting that flux depends on the angle between B and area vector, not just B and area.

Faraday's Law of Electromagnetic Induction

E = - \frac{d Φ_{B}}{d t}

When to use. Use to find induced EMF whenever magnetic flux through a circuit changes with time.

Trap. Forgetting the negative sign indicates Lenz's law direction.

Lenz's Law

E = - \frac{d Φ_{B}}{d t}

(negative sign embodies Lenz's law)

When to use. Use to determine the direction of induced current or EMF.

Trap. Thinking induced current opposes the flux itself, not the change in flux.

Motional EMF

E = B l v

(for a rod of length l moving perpendicular to B with speed v)

When to use. Use when a conductor moves through a constant magnetic field, e.g., sliding rod on rails.

Trap. Forgetting that v, B, and l must be mutually perpendicular; otherwise use $E = B l v \sin θ$ .

Eddy Currents

No simple formula; use Lenz's law and

E = - d Φ / d t

for loops

When to use. Use to explain damping in galvanometers, induction furnaces, or magnetic braking.

Trap. Thinking eddy currents only occur in ferromagnetic materials; they occur in any conductor.

Self-Inductance

E_{L} = - L \frac{d i}{d t}

L = \frac{N Φ_{B}}{i}

When to use. Use to analyze RL circuits, energy stored in inductors, or back EMF.

Trap. Forgetting that L depends only on geometry (turns, area, length) and core material, not on current.

Inductance of a Solenoid

L = μ_{0} n^{2} A l = μ_{0} \frac{N^{2}}{l} A

(for air core)

When to use. Use to compute L of a solenoid given its dimensions and turns.

Trap. Using n (turns per unit length) vs N (total turns); formula uses n or N correctly.

Mutual Inductance

E_{2} = - M \frac{d i_{1}}{d t}

M = \frac{N_{2} Φ_{21}}{i_{1}}

When to use. Use to analyze transformers or coupled circuits.

Trap. Assuming M is symmetric ( $M_{12} = M_{21}$ ) always true for linear media.

Energy Stored in an Inductor

U = \frac{1}{2} L i^{2}

When to use. Use to find energy in an inductor in DC or AC circuits.

Trap. Thinking energy is stored only while current is changing; $U = \frac{1}{2} L i^{2}$ is stored whenever $i \neq 0$ , including steady state, and depends on the instantaneous current, not on $d i / d t$ .

AC Current and Voltage

i (t) = I_{0} \sin (ω t + ϕ)

v (t) = V_{0} \sin (ω t + ϕ)

When to use. Use to describe any sinusoidal AC source or signal.

Trap. Confusing peak value with RMS value; RMS = peak/√2 for sine wave.

RMS Value

I_{rms} = \frac{I_{0}}{\sqrt{2}}

V_{rms} = \frac{V_{0}}{\sqrt{2}}

(for sine wave)

When to use. Use to compute power or compare AC with DC.

Trap. Using RMS formula for non-sinusoidal waveforms; it's different.

Reactance and Impedance

X_{L} = ω L

X_{C} = \frac{1}{ω C}

Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}

When to use. Use to analyze any series RLC circuit.

Trap. Forgetting that $X_{L}$ and $X_{C}$ depend on frequency; at resonance, $X_{L} = X_{C}$ .

Resonance in Series RLC Circuit

ω_{0} = \frac{1}{\sqrt{L C}}

f_{0} = \frac{1}{2 π \sqrt{L C}}

When to use. Use to find resonant frequency or analyze tuning circuits.

Trap. Forgetting that resonance condition is $X_{L} = X_{C}$ , not $X_{L} = R$ .

Power in AC Circuits

P_{avg} = V_{rms} I_{rms} \cos ϕ

When to use. Use to compute power consumed in any AC circuit.

Trap. Forgetting that $\cos ϕ$ is power factor; for pure L or C, $\cos ϕ = 0$ .

Transformer

\frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}} = \frac{I_{p}}{I_{s}}

(ideal, no losses)

When to use. Use to step up or step down AC voltage in power transmission.

Trap. Forgetting that transformer works only on AC, not DC.

Solving RL Circuit Transients

i (t) = \frac{V}{R} (1 - e^{- t / τ})

(charging),

i (t) = I_{0} e^{- t / τ}

(discharging),

τ = L / R

When to use. Use to find current or voltage in RL circuits during switching.

Trap. Forgetting that time constant $τ = L / R$ ; not $R / L$ .

Phasor Diagrams

V = V_{0} ∠ ϕ

I = I_{0} ∠ θ

When to use. Use to visualize phase relationships and add voltages/currents in AC circuits.

Trap. Forgetting that phasors are for same frequency only.

Quality Factor (Q-factor)

Q = \frac{ω_{0} L}{R} = \frac{1}{R} \sqrt{\frac{L}{C}}

When to use. Use to characterize resonance in RLC circuits.

Trap. Forgetting that Q is dimensionless.

Eddy Current Braking

F \propto v

(for low speeds), no simple formula

When to use. Use to explain magnetic braking in trains or roller coasters.

Trap. Thinking eddy currents always oppose motion; they do, but direction depends on Lenz's law.

Finding Induced EMF in a Rotating Coil

E = N B A ω \sin (ω t)

(for N turns, area A, angular speed ω)

When to use. Use to analyze AC generators or dynamos.

Trap. Forgetting that EMF is maximum when plane of coil is parallel to B (θ=90°).

Average EMF in Half Cycle

E_{avg} = \frac{2}{π} N B A ω

(for half cycle)

When to use. Use to find average EMF in AC generators over half rotation.

Trap. Using average over full cycle; it's zero for sinusoidal.

Inductive and Capacitive Reactance

X_{L} = ω L

X_{C} = \frac{1}{ω C}

When to use. Use to find impedance or phase in AC circuits.

Trap. Forgetting that $X_{L}$ is proportional to f, $X_{C}$ inversely proportional.

Power Factor Correction

\cos ϕ = \frac{R}{Z}

, correction capacitor

C = \frac{P (\tan ϕ_{1} - \tan ϕ_{2})}{ω V^{2}}

When to use. Use to improve efficiency in AC power systems.

Trap. Forgetting that power factor is always between 0 and 1.

Values to remember

$1 Wb = 1 T \cdot m^{2}$ Magnetic Flux
$μ_{0} = 4 π \times 10^{- 7} H/m$ Self-Inductance
$ω = 2 π f$ , $f = 50 Hz$ (India) AC Current and Voltage
$\sqrt{2} \approx 1.414$ RMS Value
$π \approx 3.14$ Average EMF in Half Cycle

Read the full chapter: Electromagnetic Induction and AC for JEE, with what JEE asks and the common traps.