Electromagnetic Induction & Alternating Currents Formula Sheet — JEE Main Physics

Every key Electromagnetic Induction & Alternating Currents formula, definition and theorem for JEE Main Physics in one place — with common examiner traps and worked examples. Free to read; blurt from memory, then check your gaps.

Syllabus — topics coveredNTA · 14 sub-topics

Electromagnetic induction
Faraday's law
Induced emf and current
Lenz's law
Eddy currents
Self and mutual inductance
Alternating currents
Peak and RMS value
Reactance and impedance
LCR series circuit
Resonance
Power in AC circuits
Wattless current
AC generator and transformer

Faraday's & Lenz's Laws

Magnetic flux

Φ = B \cdot A = B A cos θ

θ =

angle between

B

and the area normal; unit weber (Wb);

Φ = 0

when plane

∥ B

Faraday's law

ε = - N \frac{d Φ}{d t}

flux can change via B, area A, OR orientation

θ

;

N =

turns

A bar magnet approaching a coil induces a current that opposes the magnet's motion — Lenz: the induced current opposes the change.

Induced charge

q = \frac{N ΔΦ}{R}

depends ONLY on the net flux change,

not

on how fast it changes

Three ways to change flux

Change	Example
$B$ varies	magnet moves toward coil
Area $A$ varies	sliding rod on rails
Angle $θ$ varies	rotating coil (generator)

🚫 Examiner Trap · Faraday & Lenz

(1) Lenz's law

=

energy conservation; the induced current

opposes the change

, not the flux itself. (2) Induced

emf

is independent of R, but induced

current

(

ε / R

) is not. (3) Induced charge

q = N ΔΦ/ R

ignores the time taken. (4) A changing B makes a

non-conservative

E-field (

\oint E \cdot d l \neq = 0

Motional EMF & Eddy Currents

Motional emf (rod)

ε = Blv

l =

rod length,

v =

speed

⊥ B

; from Lorentz force qvB on free charges

Rotating rod / disc

ε = \frac{1}{2} B ω l^{2} = \frac{1}{2} B ω R^{2}

ω =

angular speed,

R =

rod length; one end at the axis

A conducting rod sliding on rails in a magnetic field induces an emf Blv — Sliding rod on rails: $ε = Blv$ .

Retarding force & power

F = \frac{B ^{2} l ^{2} v}{R}; P = \frac{B ^{2} l ^{2} v ^{2}}{R}

external work done

=

Joule heat dissipated (energy conservation)

⚡ Shortcut · Eddy currents

Swirling currents in bulk conductors that

oppose

the motion (Lenz)

\Rightarrow

magnetic braking, induction furnace, damping. Reduced by

laminating

the core.

🚫 Examiner Trap · Motional emf

(1)

ε = Blv

needs

v

B

and the rod mutually

⊥

— use components otherwise. (2) Rotating rod is

\frac{1}{2} B ω l^{2}

(the

\frac{1}{2}

is forgotten constantly). (3) The magnetic force

opposes

the motion, so you must do work to keep v constant. (4) Eddy losses scale with thicknes

s^{2}

— lamination cuts them.

Self & Mutual Inductance, Energy

Self-inductance

Φ = L I, ε = - L \frac{d I}{d t}; L_{so l} = \frac{μ _{0} μ _{r} N ^{2} A}{l}

L =

inductance (henry); depends only on geometry & core

Mutual inductance

ε_{2} = - M \frac{d I _{1}}{d t}; M = k L_{1} L_{2}

coupling

k \leq 1

(

k = 1

ideal);

M = μ_{0} N_{1} N_{2} A / l

for coaxial solenoids

Current growth and decay in an LR circuit with time constant tau = L/R — LR circuit: exponential growth & decay.

LR growth / decay

I = \frac{E}{R} (1 - e^{- t / τ}); I = I_{0} e^{- t / τ}, τ = \frac{L}{R}

reaches

63%

(growth) / falls to

37%

(decay) in one

τ

Energy stored

U = \frac{1}{2} L I^{2}; u = \frac{B ^{2}}{2 μ _{0}} (density)

analogous to

\frac{1}{2} C V^{2}

for a capacitor

🚫 Examiner Trap · Inductance

(1) An inductor opposes

change

in current: at

t = 0

it blocks current (acts open), at

t = \infty

it's a wire (short). (2) Series with coupling:

L = L_{1} + L_{2} \pm 2 M

(sign from aiding/opposing fluxes). (3) L depends on geometry/core

only

, not on I. (4) Energy density

B^{2} /2 μ_{0}

mirrors

\frac{1}{2} ε_{0} E^{2}

Alternating Current — RMS & R, L, C

AC quantities

i = i_{0} sin ω t; i_{r m s} = \frac{i _{0}}{2}, i_{m e an} = \frac{2 i _{0}}{π} (half cycle)

AC meters read

rms

; full-cycle mean

= 0

Phase relationship of current and voltage for pure R (in phase), L (current lags) and C (current leads) — Phase of $I$ relative to $V$ for R, L, C.

Comparative: single elements

Element	Opposition	Phase of $I$	Power
R	$R$	in phase	$i_{r m s}^{2} R$
L	$X_{L} = ω L$	lags $9 0^{\circ}$	$0$
C	$X_{C} = \frac{1}{ω C}$	leads $9 0^{\circ}$	$0$

🚫 Examiner Trap · AC & reactance

(1) Pure L or C consumes

zero

average power (I is

9 0^{\circ}

out of phase). (2)

X_{L} = ω L \propto f

(blocks high f);

X_{C} = 1/ ω C \propto 1/ f

(blocks low f / DC). (3) Meters read rms (

i_{0} / 2

), not peak. (4) At DC (

f = 0

X_{L} = 0

(wire),

X_{C} = \infty

(open).

LCR Series Circuit — Impedance

Impedance & current

Z = R^{2} + (X_{L} - X_{C})^{2}; i_{0} = \frac{e _{0}}{Z}

Z =

impedance (

Ω

); net reactance

X_{L} - X_{C}

Phase angle

tan ϕ = \frac{X _{L} - X _{C}}{R}

X_{L} > X_{C}

: inductive (I lags);

X_{L} < X_{C}

: capacitive (I leads)

Impedance triangle with R, net reactance X_L minus X_C, and impedance Z as the hypotenuse — Impedance triangle: Z, R, $(X_{L} - X_{C})$ .

Voltages add as phasors

E_{r m s} = V_{R}^{2} + (V_{L} - V_{C})^{2}

V_{R} = I R

V_{L} = I X_{L}

V_{C} = I X_{C}

Comparative: two-element circuits

Circuit	$Z$
RL	$R^{2} + X_{L}^{2}$
RC	$R^{2} + X_{C}^{2}$
LC	$∣ X_{L} - X_{C} ∣$

🚫 Examiner Trap · LCR series

(1)

V_{L}

and

V_{C}

are

18 0^{\circ}

apart

\Rightarrow

they

subtract

; add voltages as

phasors

, never algebraically (

V_{R} + V_{L} + V_{C} \neq = E

). (2)

V_{L}

V_{C}

alone can

exceed

the source voltage (at resonance). (3) Same current flows through all series elements; it's the voltages that differ in phase. (4) Use the SAME

ω

for

X_{L}

and

X_{C}

Resonance & Power in AC

Series resonance

ω_{0} = \frac{1}{L C}, f_{0} = \frac{1}{2 π L C}

ω_{0}

X_{L} = X_{C}

Z = R

(min), I max,

cos ϕ = 1

Current versus frequency peaking at the resonant frequency, sharper for smaller resistance — Sharper peak $\Rightarrow$ higher Q (smaller R).

Quality factor

Q = \frac{ω _{0} L}{R} = \frac{1}{ω _{0} CR} = \frac{1}{R} \frac{L}{C}

bandwidth

Δ ω = R / L

; high Q

=

sharp/selective

Power in AC

P = E_{r m s} I_{r m s} cos ϕ; cos ϕ = \frac{R}{Z}

cos ϕ =

power factor; only R dissipates power

Comparative: across resonance

$ω$	Nature	$cos ϕ$
$< ω_{0}$	capacitive (I leads)	$< 1$
$= ω_{0}$	resistive, $I$ max	$1$
$> ω_{0}$	inductive (I lags)	$< 1$

🚫 Examiner Trap · Resonance & power

(1) At resonance

Z = R

(minimum), so current is

maximum

— series resonance is an 'acceptor'. (2) Wattless current (

I sin ϕ

) dissipates

no

power; a

choke

(high L, low R) limits AC almost loss-free (

cos ϕ \approx 0

). (3)

V_{L} = V_{C}

at resonance (they cancel)

\Rightarrow E = V_{R}

. (4) Power uses rms values

\times cos ϕ

, not peak.

AC Generator & Transformer

AC generator

ε = NBA ω sin ω t = ε_{0} sin ω t

peak emf

ε_{0} = NBA ω

; converts mechanical

\to

electrical energy

Transformer (ideal)

\frac{V _{s}}{V _{p}} = \frac{N _{s}}{N _{p}} = \frac{I _{p}}{I _{s}}

ideal:

V_{p} I_{p} = V_{s} I_{s}

(power conserved); mutual induction,

AC only

Transformer with primary and secondary coils wound on a laminated soft-iron core — Turns ratio sets the voltage ratio.

Comparative: step-up vs step-down

	Step-up	Step-down
Turns	$N_{s} > N_{p}$	$N_{s} < N_{p}$
Voltage	$V_{s} > V_{p}$	$V_{s} < V_{p}$
Current	$I_{s} < I_{p}$	$I_{s} > I_{p}$

🚫 Examiner Trap · Generator & transformer

(1) A transformer works on

AC only

— DC gives no changing flux, no output (and burns the primary). (2) It steps voltage and current

oppositely

(power conserved), never both up. (3) Losses: copper

I^{2} R

, eddy (laminate core), hysteresis (soft iron), leakage. (4) Transmit at

high V / low I

to cut

I^{2} R

line loss.

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This Electromagnetic Induction & Alternating Currents formula sheet covers all the high-yield Physics formulas, definitions and theorems you need for JEE Main, across Electromagnetic induction, Faraday's law, Induced emf and current, Lenz's law, Eddy currents — each shown with the key result and, where useful, a worked example.

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