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Electromagnetic Induction revision notes

Every idea in the Electromagnetic Induction chapter for JEE Main, with the usual mistakes and the fast methods. Topic 1 is open to everyone; sign in free to read all 18 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that concept, and "last" is the latest year one appeared. ★ marks ideas asked 8 or more times.

Flux and Faraday's law

Magnetic flux
8× asked, last 2026
Φ=B⃗⋅A⃗=BAcos⁡θ\Phi = \vec B\cdot\vec A = BA\cos\theta
θ\theta between B⃗\vec B and the normal to the loop. Unit weber: 1 Wb = 1 T m². Uniform B⃗\vec B, flat loop.
loop (edge-on)n^\hat nB⃗\vec Bθ\theta90∘−θ90^\circ-\theta
Φ=BAcos⁡θ\Phi=BA\cos\theta with θ\theta from the normal; the angle with the plane is 90∘−θ90^\circ-\theta
  • Only the component of B⃗\vec B along the normal counts: a loop in the xyxy plane sees only BzB_z. For a bent loop add the flux through each flat part, with normals taken in one consistent sense.
  • Not the angle from the plane. θ\theta is measured from the normal. A plane at 60∘60^\circ to B⃗\vec B means θ=30∘\theta=30^\circ; B⃗\vec B lying in the plane gives Φ=0\Phi=0, not BABA.
Faraday's law
21× asked, last 2026
e=−N dΦdt,∣eavg∣=N ∣ΔΦ∣Δt,I=eRe = -N\,\frac{d\Phi}{dt},\qquad |e_{\text{avg}}| = N\,\frac{|\Delta\Phi|}{\Delta t},\qquad I=\frac{e}{R}
Φ\Phi = flux through one turn. The minus sign is Lenz's law; use magnitudes for size. 1 Wb/s = 1 V.
tt (s)BB (T)O2450.8
B(t)B(t) through a loop of area 0.050.05 m²
ttee (V)O0.04−0.02
e=−A dB/dte=-A\,dB/dt: area × slope of each segment
  • Φ(t)\Phi(t) or B(t)B(t) given as a formula: differentiate first, then put in tt. BB changing at a steady rate gives the same emf at every instant; from a BB–tt graph, emf = area × slope of that segment.
  • Changing area in a steady field: e=B dA/dte=B\,dA/dt. A circle of changing radius gives e=2πrB dr/dte=2\pi rB\,dr/dt. A wire reshaped keeps its length, so find the new area from the fixed perimeter.
  • B=B0sin⁡ωtB=B_0\sin\omega t through a fixed loop: emax⁡=NB0ωAcos⁡θe_{\max}=NB_0\omega A\cos\theta. A loop inside a solenoid carrying I0sin⁡ωtI_0\sin\omega t: emax⁡=μ0nI0ωAe_{\max}=\mu_0 nI_0\omega A, with AA the loop's own area.
  • A coaxial ring wider than a solenoid links flux only through the solenoid's own section: Φ=μ0nIπR2\Phi=\mu_0 nI\pi R^2 for any ring size. The emf follows dI/dtdI/dt and changes sign where II peaks.
Induced charge
1× asked, last 2023
Δq=N ∣ΔΦ∣R\Delta q = \frac{N\,|\Delta\Phi|}{R}
Same however fast the flux changes; RR = total resistance. A reversed field gives ΔΦ=2BA\Delta\Phi=2BA, not BABA.
Heat in the loop
8× asked, last 2026
P=e2R,H=∫e2R dt,R=ρ lπr2P=\frac{e^2}{R},\qquad H=\int\frac{e^2}{R}\,dt,\qquad R=\frac{\rho\,l}{\pi r^2}
ll = total wire length (turns × perimeter), rr = wire radius. A steady emf gives H=e2t/RH=e^2t/R.
  • Coil in a changing field: e∝NAe\propto NA while R∝NA/r2R\propto N\sqrt A/r^2, so P∝NA3/2r2P\propto NA^{3/2}r^2. More turns raise emf and resistance equally: II is independent of NN, but P∝NP\propto N.
  • Not π/ω\pi/\omega as one cycle. A cycle of B=B0sin⁡ωtB=B_0\sin\omega t lasts 2π/ω2\pi/\omega, while e2∝cos⁡2ωte^2\propto\cos^2\omega t repeats every π/ω\pi/\omega. Heat per cycle =(e02/2R)(2π/ω)=(e_0^2/2R)(2\pi/\omega), using the average power.
Also remember
  • Not SI by default: 1 G = 10−410^{-4} T and 1 cm² = 10−410^{-4} m². Many wrong options are exactly a power of ten off.

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Practise Electromagnetic Induction

14 more concepts in 4 topics

Lenz's law and eddy currents, Motional emf and the AC generator, Self-inductance and Mutual inductance. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Lenz's law and eddy currents

  • Lenz's law5×
  • Eddy currents2×

Motional emf and the AC generator

  • Rod moving in a field12×
  • Rod on rails5×
  • Loop crossing a field edge5×
  • Rotating rod and disc8×
  • Earth's field as data6×
  • Rotating coil (AC generator)11×

Self-inductance

  • Self-inductance15×
  • Long solenoid3×
  • Energy in an inductor10×

Mutual inductance

  • Mutual inductance5×
  • Coaxial solenoids2×
  • Small loop at a large loop's centre8×

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