Class 12 Physics · NCERT notes for NEET

Electromagnetic Waves: NCERT Notes, Formulas and Tricks for NEET

How Maxwell's displacement current links changing E and B fields, why that gives a self-travelling EM wave, and the full spectrum from radio to gamma rays. A short, high-scoring chapter: NEET usually asks 1-2 direct questions on $E_0/B_0=c$, displacement current, energy and momentum of the wave, or the order and uses of the bands.

• 1. Displacement current
• 2. EM waves and the electromagnetic spectrum 🔒

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Topic 1

Displacement current

A capacitor's gap is empty space, no charge ever jumps across it, yet a compass placed right next to the gap deflects while the capacitor charges.

• Ampere's law $\oint \vec{B}\cdot d\vec{l}={\mu }_{0}i$ fails for a charging capacitor: for the same loop, a surface through the wire encloses current $i$, but a pot-shaped surface through the gap encloses none.
• Inside the gap the electric field grows: $E=Q/({\epsilon }_{0}A)$, so the flux ${\Phi }_E=EA=Q/{\epsilon }_0$ changes at the rate $d{\Phi }_E/dt=i/{\epsilon }_0$.
• Maxwell added the displacement current $i_d={\epsilon }_{0}d{\Phi }_E/dt$. In the gap it is exactly equal to the conduction current $i$ in the wires.
• Ampere-Maxwell law: $\oint \vec{B}\cdot d\vec{l}={\mu }_0(i_c+i_d)$. The total current $i_c+i_d$ is continuous everywhere in the circuit.
• Displacement current is not a flow of charge, but it produces a magnetic field exactly like a conduction current. It exists even in vacuum.
• Steady (DC) fields give $i_d=0$. In the wires $i_d\approx 0$; in the gap $i_c=0$. Both can exist together in a leaky dielectric.
• Changing $\vec{B}$ makes $\vec{E}$ (Faraday) and changing $\vec{E}$ makes $\vec{B}$ (Maxwell). This two-way link lets fields travel by themselves as an EM wave.
• Maxwell's four equations: Gauss's law for $\vec{E}$, Gauss's law for $\vec{B}$ (no monopoles), Faraday's law and the Ampere-Maxwell law.
• They predicted a wave speed $c=1/\sqrt{{\mu }_0{\epsilon }_0}\approx 3\times 10^8$ m/s, equal to the measured speed of light: light is an EM wave.
• Hertz (1887) first produced and detected EM waves; J.C. Bose made waves of 25 mm to 5 mm; Marconi sent them over long distances.

Formulas

• $i_d={\epsilon }_0\frac{d{\Phi }_E}{dt}$
  displacement current; ${\Phi }_E$ = electric flux
• $i_d={\epsilon }_{0}A\frac{dE}{dt}=C\frac{dV}{dt}$
  parallel-plate capacitor, plate area A, $C={\epsilon }_{0}A/d$
• $\oint \vec{E}\cdot d\vec{A}=\frac{Q}{{\epsilon }_0}$
  Gauss's law (electricity)
• $\oint \vec{B}\cdot d\vec{A}=0$
  Gauss's law (magnetism): no magnetic monopoles
• $\oint \vec{E}\cdot d\vec{l}=-\frac{d{\Phi }_B}{dt}$
  Faraday's law
• $\oint \vec{B}\cdot d\vec{l}={\mu }_0{i}_c+{\mu }_0{\epsilon }_0\frac{d{\Phi }_E}{dt}$
  Ampere-Maxwell law
• $B=\frac{{\mu }_0{i}_{d}r}{2\pi R^2}(r<R),B=\frac{{\mu }_0{i}_d}{2\pi r}(r>R)$
  field in and around the gap of a circular-plate capacitor of radius R

Tips, tricks and hacks

Common mistakes

NEET traps

"Displacement current has the same magnitude as conduction current in the leads" is TRUE, even though it is not a flow of charge.

NEET asks for $i_d$ for $E=E_0\sin \omega t$ between plates: $i_d={\epsilon }_{0}A\omega E_0\cos \omega t$; the peak is ${\epsilon }_{0}A\omega E_0$. Do not forget the factor $\omega$.

Which law of Maxwell's set says magnetic monopoles do not exist? Gauss's law for magnetism, $\oint \vec{B}\cdot d\vec{A}=0$, not Faraday's law.

Practise Electromagnetic Waves questions

Topic-wise practice from Level 1 to Level 3, NCERT-based questions and NEET PYQs, with a full solution after every answer.