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Electromagnetic Waves revision notes

Every idea in the Electromagnetic Waves chapter for JEE Main, with the usual mistakes and the fast methods. Topic 1 is open to everyone; sign in free to read all 20 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.

Displacement current and Maxwell's equations

Displacement current
8× asked, last 2026
Id=ε0dΦEdt=ε0AdEdt=CdVdtI_d=\varepsilon_0\frac{d\Phi_E}{dt}=\varepsilon_0 A\frac{dE}{dt}=C\frac{dV}{dt}
Air gap, plate area AA; dielectric: ε0→Kε0\varepsilon_0\to K\varepsilon_0, C dV/dtC\,dV/dt holds. Equals the wire current at all times.
IIIIId=ε0 dΦE/dtI_d=\varepsilon_0\,d\Phi_E/dtgrowing E⃗\vec E
Charging: the wire carries II, the gap carries an equal displacement current
  • On AC, V=V0sin⁡ωtV=V_0\sin\omega t gives peak Id=CV0ωI_d=CV_0\omega and rms CVrmsωCV_{\text{rms}}\omega, equal to the wire current. A patch of area A0A_0 between the plates carries IdA0/AI_dA_0/A.
  • Not ff in place of ω\omega. Use ω=2πf\omega=2\pi f. Not the rms or peak-to-peak voltage when the peak current is asked: in V0sin⁡ωtV_0\sin\omega t the amplitude is V0V_0.
Magnetic field between the plates
B=μ0Id r2πR2  (r<R),B=μ0Id2πr  (r≥R)B=\frac{\mu_0 I_d\, r}{2\pi R^2}\;(r<R),\qquad B=\frac{\mu_0 I_d}{2\pi r}\;(r\ge R)
Circular plates of radius RR, rr from the axis. For r≥Rr\ge R it equals the field of the wire.
rrBBORRμ0Id/2πR\mu_0I_d/2\pi R∝r\propto ras for the wire
Inside the plates BB grows as rr; outside it is the wire's μ0I/2πr\mu_0I/2\pi r
Conduction vs displacement current
2× asked, last 2026
Jc=σE,Jd=ε∂E∂t,Jc,max⁡Jd,max⁡=σωεJ_c=\sigma E,\qquad J_d=\varepsilon\frac{\partial E}{\partial t},\qquad \frac{J_{c,\max}}{J_{d,\max}}=\frac{\sigma}{\omega\varepsilon}
E=E0sin⁡ωtE=E_0\sin\omega t, σ=1/ρ\sigma=1/\rho, ε=Kε0\varepsilon=K\varepsilon_0. At time tt, Jc/Jd=tan⁡ωt/ρεωJ_c/J_d=\tan\omega t/\rho\varepsilon\omega.
Maxwell's equations
5× asked, last 2026
∮E⃗⋅dA⃗=qencε0,∮B⃗⋅dA⃗=0∮E⃗⋅dl⃗=−dΦBdt,∮B⃗⋅dl⃗=μ0(Ic+ε0dΦEdt)\begin{gathered}\oint\vec E\cdot d\vec A=\frac{q_{\text{enc}}}{\varepsilon_0},\qquad \oint\vec B\cdot d\vec A=0\\ \oint\vec E\cdot d\vec l=-\frac{d\Phi_B}{dt},\qquad \oint\vec B\cdot d\vec l=\mu_0\Big(I_c+\varepsilon_0\frac{d\Phi_E}{dt}\Big)\end{gathered}
Gauss (E), Gauss (B), Faraday, Ampère–Maxwell. ε0 dΦE/dt\varepsilon_0\,d\Phi_E/dt (displacement current) has units of current.
  • E⃗\vec E over a closed surface: Gauss. E⃗\vec E round a loop =−dΦB/dt=-d\Phi_B/dt: Faraday. ∮B⃗⋅dA⃗=0\oint\vec B\cdot d\vec A=0: no monopoles. B⃗\vec B round a loop: Ampère, Ampère–Maxwell if ε0 dΦE/dt\varepsilon_0\,d\Phi_E/dt is added.
  • Not ∮E⃗⋅dl⃗=0\oint\vec E\cdot d\vec l=0 or ∮B⃗⋅dl⃗=μ0I\oint\vec B\cdot d\vec l=\mu_0I for changing fields. These are static-only. Faraday and Ampère–Maxwell carry the time derivatives; Gauss's laws hold always.

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Practise Electromagnetic Waves

16 more concepts in 5 topics

Nature and speed of EM waves; Wave equation and directions; Energy and intensity; Momentum, pressure and force on charges; and Electromagnetic spectrum. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Nature and speed of EM waves

  • Nature of EM waves5×
  • Speed in vacuum and in a medium15×
  • E–B relation31×

Wave equation and directions

  • Directions of E, B and travel31×
  • Plane-wave equation15×

Energy and intensity

  • Energy density7×
  • Average energy density7×
  • Intensity11×
  • Point source6×

Momentum, pressure and force on charges

  • Momentum of an EM wave4×
  • Radiation pressure and force6×
  • Force on a charge in the wave6×

Electromagnetic spectrum

  • Order of the spectrum7×
  • Wavelength ranges2×
  • Sources and detectors3×
  • Uses1×

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About 135 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

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