Physics · Electromagnetism

Electromagnetic Induction and Alternating Currents formulas for JEE

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

35 formulas4 concepts

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QuestionState the formula — Total Charge Flown

Reveal answer

Total Charge Flown

\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

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All 35 Electromagnetic Induction and Alternating Currents formulas

Electromagnetic Induction

9 formulas

Total Charge Flown

\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

\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)

\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)

\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

\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

\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)

\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)

\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)

\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

Inductance and AC Generator

12 formulas

Decay of Current in LR Circuit

I(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) = \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

\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

u_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

U_B = \frac{1}{2} L I^2

Energy stored in the magnetic field of an inductor.

applies whenLinear inductor.

energyinductormagnetic

AC Generator EMF

\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

N_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

\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 = \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

N \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

\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 = \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

Alternating Currents

11 formulas

AC Current Equation

i = i_m \sin(\omega t + \phi)

Instantaneous alternating current equation with phase difference.

applies whenSteady state AC.

accurrentphase

AC Voltage Equation

v = v_m \sin \omega t

Instantaneous alternating voltage equation.

applies whenSinusoidal variation.

acvoltageinstantaneous

Capacitive Reactance

X_C = \frac{1}{\omega C}

Opposition to AC current flow by a capacitor.

applies whenIdeal capacitor.

reactancecapacitorac

Impedance of LCR Circuit

Z = \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

X_L = \omega L

Opposition to AC current flow by an inductor.

applies whenIdeal inductor.

reactanceinductorac

Charge in LC Oscillations

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

Measure of sharpness of resonance in an LCR circuit.

applies whenSeries LCR circuit.

quality factorresonancebandwidth

Resonant Frequency

\omega_0 = \frac{1}{\sqrt{LC}}

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

applies when

X_L = X_C

resonancefrequencylcr

RMS Current

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

Root mean square value of sinusoidal AC current.

applies whenSinusoidal waveform only.

rmscurrentac

RMS Voltage

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

Root mean square value of sinusoidal AC voltage.

applies whenSinusoidal waveform only.

rmsvoltageac

Power in AC Circuits

3 formulas

Average AC Power

P = 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 \phi = \frac{R}{Z}

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

applies whenSeries LCR circuit.

power factoracimpedance

Wattless Current

I_q = I_{rms} \sin \phi

Component of AC current that does not consume average power.

applies whenCurrent in inductor or capacitor.

wattlesscurrentac

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