Multiple Choice & Assertion-Reason

PHYExam Practice

This is a chapter-wide rapid-revision article for the one-mark MCQ and Assertion-Reason items on electromagnetic waves. The recurring ideas are Maxwell's displacement current, the speed $c=1/\sqrt{\mu_0\varepsilon_0}$ , the transverse nature of EM waves with $E_0=cB_0$ , the equality of electric and magnetic energy densities, radiation pressure, and the ordering of the EM spectrum.

These appear every year because they test definitions and ratios rather than long calculation.

Speed of EM wave in vacuum

c = \dfrac{1}{\sqrt{\mu_0 \varepsilon_0}}

\mu_0 = 4\pi\times10^{-7}\ \text{T m A}^{-1}

\varepsilon_0 = 8.85\times10^{-12}\ \text{C}^{2}\,\text{N}^{-1}\,\text{m}^{-2}

c\approx 3\times10^{8}\ \text{m s}^{-1}

Displacement current

I_d = \varepsilon_0 \dfrac{d\Phi_E}{dt}

\Phi_E

is electric flux;

I_d

has the same dimensions and SI unit (ampere) as conduction current.

Field amplitude ratio

\dfrac{E_0}{B_0} = c

E_0,B_0

are peak field magnitudes; the same ratio holds for instantaneous and rms values:

E/B = E_{rms}/B_{rms} = c

Radiation pressure (reflecting surface)

P_{rad} = \dfrac{2I}{c}

I

is intensity; for a perfectly absorbing surface

P_{rad}=I/c

Displacement current arises from a time-varying electric field ( $d\Phi_E/dt$ ), not from any steady or constant field; it acts in the gap of a charging capacitor where there is no charge motion.
$I_d$ is a current only in its magnetic effect: it has the SI unit ampere and makes Ampere's circuital law continuous: $\oint \vec B\cdot d\vec l = \mu_0(I_c+I_d)$ .
EM waves are transverse: $\vec E$ , $\vec B$ and the propagation direction $\hat k$ are mutually perpendicular, with $\vec E\times\vec B$ along $\hat k$ .
In an EM wave the electric and magnetic average energy densities are exactly equal, $\langle u_E\rangle = \langle u_B\rangle$ , so the total energy is shared half-and-half.
Spectrum by increasing frequency (decreasing wavelength): radio < microwave < infrared < visible < ultraviolet < X-ray < gamma; gamma rays have the shortest $\lambda$ and highest energy.
Infrared is used in TV remotes and thermal imaging (heat detection); microwaves in radar and ovens; UV causes tanning; X-rays for imaging.
EM waves carry both energy and momentum, so they exert radiation pressure; a reflecting surface receives twice the pressure of an absorbing one for the same intensity.
For Assertion-Reason, decide truth of A and R separately, then ask whether R explains A: e.g. transversality (A) is correctly explained by $\vec E$ and $\vec B$ being mutually perpendicular to $\hat k$ (R).

Where the marks go

Writing $c=\sqrt{\mu_0\varepsilon_0}$ or $c=1/(\mu_0\varepsilon_0)$ instead of $c=1/\sqrt{\mu_0\varepsilon_0}$ — both the reciprocal and the square root must be present.
Saying $u_E$ is twice or half of $u_B$ : the two average energy densities are equal in a free EM wave.
Mixing up the radiation-pressure factors — using $I/c$ for a reflector (should be $2I/c$ ) or $2I/c$ for an absorber (should be $I/c$ ).
Calling displacement current the same as conduction current in nature; they share units and the magnetic effect, but $I_d$ needs no moving charge.

How the board asks it

Assertion–Reasondisplacement current in a charging capacitor
Assertion (A): A displacement current flows in the gap between the plates of a charging capacitor even though no charge crosses the gap. Reason (R): Displacement current arises from a time-varying electric flux $d\Phi_E/dt$ , not from the motion of charge. Choose the correct option: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.
Assertion–Reasontransverse nature and $\vec E\times\vec B$ along $\hat k$
Assertion (A): Electromagnetic waves are transverse in nature. Reason (R): In an electromagnetic wave the electric field $\vec E$ , the magnetic field $\vec B$ and the direction of propagation $\hat k$ are mutually perpendicular, with $\vec E\times\vec B$ along $\hat k$ . Choose the correct option: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.
Assertion–Reasonspeed $c=1/\sqrt{\mu_0\varepsilon_0}$
Assertion (A): All electromagnetic waves travel through vacuum with the same speed $c$ . Reason (R): The speed of an electromagnetic wave in vacuum is fixed by the constants of free space as $c=1/\sqrt{\mu_0\varepsilon_0}$ and is independent of frequency. Choose the correct option: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.
Assertion–Reasonordering of the EM spectrum by frequency and energy
Assertion (A): Gamma rays have the shortest wavelength and the highest energy among electromagnetic waves. Reason (R): Photon energy increases with frequency, and gamma rays have the highest frequency in the electromagnetic spectrum. Choose the correct option: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.
Assertion–Reason $\langle u_E\rangle=\langle u_B\rangle$ energy density equality
Assertion (A): In a plane electromagnetic wave travelling in vacuum, the average energy carried by the electric field equals that carried by the magnetic field. Reason (R): The average electric and magnetic energy densities satisfy $\langle u_E\rangle=\langle u_B\rangle$ because $E_0=cB_0$ . Choose the correct option: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.
Assertion–Reasonradiation pressure on a reflector vs absorber
Assertion (A): For the same intensity, a perfectly reflecting surface experiences twice the radiation pressure of a perfectly absorbing surface. Reason (R): Electromagnetic waves carry momentum, and on reflection the momentum change of the wave is doubled compared with absorption. Choose the correct option: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

PreviousWavelength, Frequency & Spectrum

Written for Sublevo. Question text quoted anywhere in these notes is the Council’s and carries its year and paper; the board’s own diagrams are not reproduced.