JEE Physics Electromagnetic Waves MCQs Set 04

Answer: (c) Gamma rays

Explanation:
1. Energy per photon \( E=\frac{15\times10^3}{10^{16}}=1.5\times10^{-12}\ \text{J} \).
2. Frequency \( f=\frac Eh=\frac{1.5\times10^{-12}}{6\times10^{-34}}=2.5\times10^{21}\ \text{Hz} \).
3. This is far above the X-ray range (up to about 10¹⁹ Hz), so the radiation is gamma rays.

Teacher's Note:
1. Power divided by photon rate gives the energy of each photon.
2. Gamma rays have frequencies above about 10¹⁹ Hz.

Answer: (a) \( \frac1\omega\left(\vec K\times\vec E\right) \)

Explanation:
1. The wave direction is \( \vec E\times\vec B \), so \( \vec B\parallel\hat k\times\vec E \) with \( B=\frac Ec \).
2. Since \( K=\frac\omega c \): \( \vec B=\frac{\hat k\times\vec E}{c}=\frac{\vec K\times\vec E}{\omega} \).

Teacher's Note:
1. E, B and the propagation direction are mutually perpendicular.
2. c = ω/K links the two forms.

Answer: (a) \( kE_0=\omega B_0 \)

Explanation:
1. In vacuum \( \frac{E_0}{B_0}=c=\frac\omega k \).
2. \( kE_0=\omega B_0 \).

Teacher's Note:
1. The ratio of the amplitudes is the speed of light.
2. The phase speed is ω/k.

Answer: (a) Positive direction of x

Explanation:
1. The direction of propagation is that of \( \vec E\times\vec B \).
2. We need \( \hat j\times\vec B=-\hat k \). Since \( \hat j\times\hat i=-\hat k \), B points along the positive x direction.

Teacher's Note:
1. Use the right-hand rule on E x B = direction of energy flow.
2. B is perpendicular to both E and the propagation direction.

Answer: (a) A-IV, B-I, C-II, D-III

Explanation:
1. Gauss's law in electrostatics is the flux of E equal to q/ε0 (IV).
2. Faraday's law relates the line integral of E to the rate of change of magnetic flux (I).
3. Gauss's law in magnetism says the net magnetic flux is zero (II).
4. The Ampere-Maxwell law includes the displacement current term (III).

Teacher's Note:
1. These are Maxwell's four equations in integral form.
2. Only the Ampere-Maxwell law contains the term μ0ε0 dφE/dt.

Answer: (a) Statement I is true but Statement II is false

Explanation:
1. Statement I is true: EM waves carry no charge, so static fields do not deflect them.
2. Statement II is false: the correct relation is \( E_0=cB_0=\frac{B_0}{\sqrt{\mu_0\varepsilon_0}} \). The quantity \( \sqrt{\mu_0/\varepsilon_0} \) is the impedance of free space (about 377 ohm), not the speed of light.

Teacher's Note:
1. E0/B0 has the dimensions of a speed.
2. Photons are neutral, so they are not deflected by static fields.

Answer: (b) \( \frac1{40\pi}\ \text{W/m}^2 \)

Explanation:
1. Light power \( =0.05\times100=5\ \text{W} \).
2. Total intensity at 5 m: \( I=\frac{5}{4\pi(5)^2}=\frac1{20\pi}\ \text{W/m}^2 \).
3. The energy of an EM wave is shared equally between the electric and magnetic fields, so the electric part gives \( \frac12\times\frac1{20\pi}=\frac1{40\pi}\ \text{W/m}^2 \).

Teacher's Note:
1. Intensity = power / area of the sphere.
2. Average electric and magnetic energy densities are equal.

Answer: (c) A-IV, B-III, C-I, D-II

Explanation:
1. Microwaves are used in radar for aircraft navigation (IV).
2. UV rays are used in Lasik eye surgery (III).
3. Infra-red rays are used in physiotherapy (I).
4. X-rays (and gamma rays) are used in the treatment of cancer (II).

Teacher's Note:
1. Match the radiation to its most common application.
2. Higher energy radiations are used for destroying tissue (cancer treatment).

Answer: (b) A-IV, B-I, C-II, D-III

Explanation:
1. Microwaves are produced by klystron or magnetron valves (IV).
2. Gamma rays come from radioactive decay of nuclei (I).
3. Radio waves are produced by rapidly accelerating and decelerating electrons in aerials (II).
4. X-rays are produced by transitions of inner shell electrons (III).

Teacher's Note:
1. Think about the source of each radiation.
2. Electron transitions in inner shells have high energy, giving X-rays.

Answer: (d) \( \frac12 \)

Explanation:
1. In an EM wave the electric and magnetic energy densities are equal on average: \( u_E=u_B=\frac12\varepsilon_0E_{rms}^2 \).
2. \( \frac{u_E}{u_E+u_B}=\frac12 \).

Teacher's Note:
1. Energy is shared equally between the electric and the magnetic field.
2. Total energy density = ε0 E²_rms.