Physics · Electromagnetism

Electromagnetic Induction and Alternating Currents formulas for JEE

Every Electromagnetic Induction and Alternating Currents formula you need for JEE, grouped by concept.

FormulasRevision notes
35 formulas4 concepts
01Electromagnetic Induction02Inductance and AC Generator03Alternating Currents04Power in AC Circuits
01

Electromagnetic Induction

9 formulas

Total Charge Flown

Δq=ΔΦR\Delta q = \frac{\Delta \Phi}{R}

Total induced charge flown through a circuit is independent of time.

applies whenClosed circuit of resistance R.
jee-advancedcharge flownfluxresistance

Faraday's Law of Induction

ε=−NdΦBdt\varepsilon = -N \frac{d\Phi_B}{dt}

The induced EMF in a coil of N turns is the negative rate of change of magnetic flux.

applies whenClosed coil/loop.
faradayinductionemflenz

Magnetic Flux (Uniform Field)

ΦB=B⋅A=BAcos⁡θ\Phi_B = \mathbf{B} \cdot \mathbf{A} = BA \cos \theta

Magnetic flux through a plane surface area in a uniform magnetic field.

applies whenUniform magnetic field.
fluxmagnetic fieldscalar product

Magnetic Flux (Non-Uniform Field)

ΦB=∫B⋅dA\Phi_B = \int \mathbf{B} \cdot d\mathbf{A}

Magnetic flux through a surface for a varying magnetic field.

applies whenGeneral case.
fluxintegrationnon-uniform

Induced Electric Field

∮E⋅dl=−dΦBdt\oint \mathbf{E} \cdot d\mathbf{l} = -\frac{d\Phi_B}{dt}

Non-conservative electric field induced by a time-varying magnetic flux.

applies whenTime-varying magnetic field.
jee-advancedinduced electric fieldnon-conservative

Lorentz Force

F=q(E+v×B)\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})

Total force experienced by a charge moving in electric and magnetic fields.

applies whenGeneral case.
lorentzforcemoving charge

Motional EMF (Straight Rod)

ε=Blv\varepsilon = Blv

EMF induced in a straight conductor moving perpendicularly through a uniform magnetic field.

applies whenB, l, and v are mutually perpendicular.
motional emfconductorvelocity

Motional EMF (Rotating Rod)

ε=12BωR2\varepsilon = \frac{1}{2} B \omega R^2

EMF induced between the center and rim of a rod rotating in a uniform magnetic field.

applies whenUniform magnetic field parallel to the axis of rotation.
motional emfrotationangular velocity

Motional EMF (Vector Form)

ε=∫(v×B)⋅dl\varepsilon = \int (\mathbf{v} \times \mathbf{B}) \cdot d\mathbf{l}

General vector integral form for motional EMF in an arbitrary conductor.

applies whenArbitrary shape and velocity.
jee-advancedmotional emfvectorintegration
02

Inductance and AC Generator

12 formulas

Decay of Current in LR Circuit

I(t)=I0e−Rt/LI(t) = I_0 e^{-Rt/L}

Current decay in a shorted LR circuit.

applies whenSource removed at t=0.
jee-advancedlr circuitdecaytransient

Growth of Current in LR Circuit

I(t)=VR(1−e−Rt/L)I(t) = \frac{V}{R} (1 - e^{-Rt/L})

Current buildup in a DC circuit with an inductor and a resistor.

applies whenDC voltage source applied at t=0.
jee-advancedlr circuitgrowthtransient

Transformer Ratio

VsVp=NsNp=IpIs\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}

Relation between primary/secondary voltages, turns, and currents in an ideal transformer.

applies whenIdeal transformer (100% efficiency, no flux leakage).
transformervoltagecurrent

Magnetic Energy Density

uB=B22μ0u_B = \frac{B^2}{2\mu_0}

Energy stored per unit volume in a magnetic field.

applies whenVacuum or non-magnetic medium.
energy densitymagnetic field

Magnetic Energy in Inductor

UB=12LI2U_B = \frac{1}{2} L I^2

Energy stored in the magnetic field of an inductor.

applies whenLinear inductor.
energyinductormagnetic

AC Generator EMF

ε=NBAωsin⁡(ωt)\varepsilon = NBA\omega \sin(\omega t)

Instantaneous EMF produced by an AC generator rotating at constant angular velocity.

applies whenConstant angular velocity.
generatoracemf

Mutual Inductance Flux Linkage

N1Φ1=M12I2N_1 \Phi_1 = M_{12} I_2

Magnetic flux linkage in one coil due to current in another.

applies whenLinear magnetic medium.
mutual inductanceflux linkage

Mutual Induced EMF

ε1=−MdI2dt\varepsilon_1 = -M \frac{dI_2}{dt}

EMF induced in one coil due to a changing current in a neighboring coil.

applies whenConstant mutual inductance.
mutual inductionemfcoupled coils

Mutual Inductance of Co-axial Solenoids

M=μrμ0n1n2πr12lM = \mu_r \mu_0 n_1 n_2 \pi r_1^2 l

Mutual inductance between two long co-axial solenoids with a core.

applies whenLong solenoids where edge effects are ignored, inner radius r_1.
mutual inductancesolenoidcore

Self Inductance Flux Linkage

NΦB=LIN \Phi_B = L I

Total magnetic flux linkage of a coil related to its own current.

applies whenLinear magnetic medium.
self inductanceflux linkage

Self Induced EMF

ε=−LdIdt\varepsilon = -L \frac{dI}{dt}

Back EMF induced in a coil opposing the change in its own current.

applies whenConstant self-inductance.
self inductionemfinductor

Self Inductance of a Solenoid

L=μrμ0n2AlL = \mu_r \mu_0 n^2 A l

Self-inductance of a long solenoid filled with a material of relative permeability.

applies whenLong solenoid, ignoring edge effects.
self inductancesolenoid
Reading a formula once isn't the same as recalling it in the exam. Rhovecs tracks which of these you've seen and brings them back on a forgetting schedule.See how it works
03

Alternating Currents

11 formulas

AC Current Equation

i=imsin⁡(ωt+ϕ)i = i_m \sin(\omega t + \phi)

Instantaneous alternating current equation with phase difference.

applies whenSteady state AC.
accurrentphase

AC Voltage Equation

v=vmsin⁡ωtv = v_m \sin \omega t

Instantaneous alternating voltage equation.

applies whenSinusoidal variation.
acvoltageinstantaneous

Capacitive Reactance

XC=1ωCX_C = \frac{1}{\omega C}

Opposition to AC current flow by a capacitor.

applies whenIdeal capacitor.
reactancecapacitorac

Impedance of LCR Circuit

Z=R2+(XL−XC)2Z = \sqrt{R^2 + (X_L - X_C)^2}

Total effective opposition to current in a series LCR circuit.

applies whenSeries connection of L, C, and R.
impedancelcrac

Inductive Reactance

XL=ωLX_L = \omega L

Opposition to AC current flow by an inductor.

applies whenIdeal inductor.
reactanceinductorac

Charge in LC Oscillations

q(t)=q0cos⁡(ω0t)q(t) = q_0 \cos(\omega_0 t)

Simple harmonic oscillation of charge in an ideal LC circuit.

applies whenIdeal LC circuit with no resistance.
jee-advancedlc oscillationschargeshm

Phase Angle in LCR

tan⁡ϕ=XL−XCR\tan \phi = \frac{X_L - X_C}{R}

Phase difference between voltage and current in an LCR circuit.

applies whenVoltage leading current defined as positive.
phaselcrac

Quality Factor (Q-factor)

Q=1RLCQ = \frac{1}{R} \sqrt{\frac{L}{C}}

Measure of sharpness of resonance in an LCR circuit.

applies whenSeries LCR circuit.
quality factorresonancebandwidth

Resonant Frequency

ω0=1LC\omega_0 = \frac{1}{\sqrt{LC}}

Angular frequency at which an LC or LCR circuit resonates (minimum impedance).

applies whenXL=XCX_L = X_C.
resonancefrequencylcr

RMS Current

Irms=im2I_{rms} = \frac{i_m}{\sqrt{2}}

Root mean square value of sinusoidal AC current.

applies whenSinusoidal waveform only.
rmscurrentac

RMS Voltage

Vrms=vm2V_{rms} = \frac{v_m}{\sqrt{2}}

Root mean square value of sinusoidal AC voltage.

applies whenSinusoidal waveform only.
rmsvoltageac
04

Power in AC Circuits

3 formulas

Average AC Power

P=VrmsIrmscos⁡ϕP = V_{rms} I_{rms} \cos \phi

Average power dissipated in an AC circuit over a full cycle.

applies whenSteady state AC.
poweraverageac

Power Factor

cos⁡ϕ=RZ\cos \phi = \frac{R}{Z}

Ratio of real power to apparent power in an AC circuit.

applies whenSeries LCR circuit.
power factoracimpedance

Wattless Current

Iq=Irmssin⁡ϕI_q = I_{rms} \sin \phi

Component of AC current that does not consume average power.

applies whenCurrent in inductor or capacitor.
wattlesscurrentac
Other chapters
PhysicsUnits and Measurements4 formulasPhysicsKinematics43 formulasPhysicsLaws of Motion30 formulasPhysicsWork Energy and Power29 formulasPhysicsRotational Motion49 formulasPhysicsGravitation29 formulasPhysicsProperties of Solids and Liquids63 formulasPhysicsThermodynamics32 formulasPhysicsKinetic Theory of Gases29 formulasPhysicsOscillations and Waves39 formulasPhysicsElectrostatics48 formulasPhysicsCurrent Electricity54 formulasPhysicsMagnetic Effects of Current and Magnetism37 formulasPhysicsElectromagnetic Waves25 formulasPhysicsOptics55 formulasPhysicsDual Nature of Matter and Radiation17 formulasPhysicsAtoms and Nuclei27 formulasPhysicsElectronic Devices27 formulas

Rhovecs schedules these formulas back to you right before you’d forget them — and picks the next concept to practise. We decide, you execute.

Get started