CBSE Class 12 Physics Electromagnetic Waves MCQs Set 07

Answer: (c) 2 A

Explanation:
1. i_d = \( \frac{dQ}{dt} \) = C \( \frac{dV}{dt} \)
2. i_d = 2 × 10⁻⁶ × 10⁶ = 2 A

Teacher's Note:
1. The displacement current between the plates equals the conduction current in the leads.
2. Convert μF to F before multiplying.

Answer: (b) the electric field changes with time

Explanation:
1. i_d = ε₀ \( \frac{d\Phi_E}{dt} \), so it is non-zero only when the electric flux changes.
2. Displacement current arises wherever the electric field changes with time.

Teacher's Note:
1. It needs no moving charges; it exists even in vacuum.
2. A constant field, however strong, gives zero displacement current.

Answer: (a) 1.6 × 10⁻⁷ T

Explanation:
1. B₀ = \( \frac{E_0}{c} \) = \( \frac{48}{3 \times 10^8} \)
2. B₀ = 1.6 × 10⁻⁷ T

Teacher's Note:
1. Divide by c, do not multiply; 1.44 × 10¹⁰ T comes from multiplying.
2. The magnetic field of an EM wave is always numerically tiny.

Answer: (d) 1.5 × 10¹⁰ Hz

Explanation:
1. The distance between consecutive crests is one wavelength: λ = 2 cm = 0.02 m.
2. ν = \( \frac{c}{\lambda} \) = \( \frac{3 \times 10^8}{0.02} \) = 1.5 × 10¹⁰ Hz

Teacher's Note:
1. Crest to next crest is λ; crest to next trough is only λ/2.
2. Waves of a few centimetres lie in the microwave region.

Answer: (a) +x direction

Explanation:
1. The direction of propagation is along \( \vec{E} \times \vec{B} \).
2. \( \hat{j} \times \hat{k} = \hat{i} \), so the wave travels along the +x direction.

Teacher's Note:
1. The wave can never travel along E or along B, because it is transverse.
2. Use the cyclic order x → y → z → x for cross products.

Answer: (b) 1.26 cm

Explanation:
1. Comparing with sin(kx + ωt), k = 500 m⁻¹.
2. λ = \( \frac{2\pi}{k} \) = \( \frac{2\pi}{500} \) = 0.01257 m ≈ 1.26 cm
3. Check: \( \frac{\omega}{k} \) = \( \frac{1.5 \times 10^{11}}{500} \) = 3 × 10⁸ m s⁻¹ = c.

Teacher's Note:
1. k is the number in front of x, not the wavelength itself.
2. The + sign between the terms means the wave moves along −x.

Answer: (c) 1.5 × 10⁸ m s⁻¹

Explanation:
1. v = \( \frac{1}{\sqrt{\mu \varepsilon}} \) = \( \frac{c}{\sqrt{\mu_r \varepsilon_r}} \)
2. v = \( \frac{3 \times 10^8}{\sqrt{1 \times 4}} \) = 1.5 × 10⁸ m s⁻¹

Teacher's Note:
1. Take the square root of ε_r; dividing by 4 gives the trap 7.5 × 10⁷ m s⁻¹.
2. The speed in any material medium is less than c.

Answer: (b) Microwaves, infrared, ultraviolet, gamma rays

Explanation:
1. Wavelength decreases in the order radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays.
2. Only microwaves, infrared, ultraviolet, gamma rays follows this order.

Teacher's Note:
1. Decreasing wavelength means increasing frequency.
2. Option (a) is in increasing wavelength order, the reverse of what is asked.

Answer: (d) microwaves

Explanation:
1. Radar needs short radio waves that travel in a straight line and reflect well from aircraft.
2. These are microwaves, produced by klystrons, magnetrons and Gunn diodes.

Teacher's Note:
1. Speed guns used by traffic police also use microwaves.
2. Microwaves have wavelengths from about 1 mm to 0.1 m.

Answer: (a) ultraviolet radiation from the Sun

Explanation:
1. Ozone strongly absorbs ultraviolet radiation.
2. Without it, harmful ultraviolet radiation from the Sun would reach the ground in large amounts.

Teacher's Note:
1. Too much UV causes skin damage and harms the eyes.
2. Infrared trapped by the atmosphere is linked with the greenhouse effect, not the ozone layer.

Answer: (b) matches a resonant frequency of water molecules

Explanation:
1. The oven uses microwaves of about 2.45 GHz, which matches a resonant frequency of water molecules.
2. Water in the food absorbs the energy efficiently and heats up. Answer: matches a resonant frequency of water molecules.

Teacher's Note:
1. The container is not heated directly, because it has little water.
2. Energy transfer is most efficient at resonance.

Answer: (d) 3 × 10⁻⁸ kg m s⁻¹

Explanation:
1. For complete absorption, p = \( \frac{U}{c} \)
2. p = \( \frac{9}{3 \times 10^8} \) = 3 × 10⁻⁸ kg m s⁻¹

Teacher's Note:
1. 6 × 10⁻⁸ would be the answer for a perfectly reflecting surface (2U/c).
2. The tiny value explains why we do not feel the push of light.

Answer: (c) an accelerated charge

Explanation:
1. A charge at rest gives only an electric field; a charge moving uniformly gives a steady magnetic field as well, but no waves.
2. Only an accelerated charge produces changing E and B fields that travel out as a wave.

Teacher's Note:
1. An oscillating charge is a common example of an accelerated charge.
2. The frequency of the wave equals the frequency of oscillation of the charge.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Between the plates of a charging capacitor there is vacuum or an insulator, so no charges move there, yet a displacement current exists. The Assertion is correct.
2. i_d = ε₀ dΦ_E/dt, so it comes from a changing electric flux. The Reason is correct.
3. Since it depends only on the changing flux, not on moving charges, the Reason explains the Assertion.

Teacher's Note:
1. Displacement current produces a magnetic field just like conduction current.
2. Its unit is still the ampere.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. A transverse wave is one in which the oscillation is perpendicular to the direction of travel. EM waves are transverse, so the Assertion is correct.
2. E, B and the direction of propagation are mutually perpendicular, so the Reason is correct.
3. The Reason is exactly why EM waves are called transverse.

Teacher's Note:
1. The direction of travel is along E × B.
2. Sound in air is longitudinal, unlike light.

Answer: (c) A is true, but R is false.

Explanation:
1. Light from the Sun reaches us through the vacuum of space, so the Assertion is correct.
2. EM waves consist of oscillating electric and magnetic fields and need no medium. They are not mechanical waves, so the Reason is false.

Teacher's Note:
1. The fields regenerate each other, so no medium is needed.
2. Mechanical waves such as sound cannot travel in vacuum.

Answer: (d) A is false, but R is true.

Explanation:
1. u_E = ½ε₀E² and u_B = B²/2μ₀. Putting B = E/c and c² = 1/μ₀ε₀ gives u_B = ½ε₀E² = u_E.
2. So the energy is shared equally; the Assertion is false and the Reason is true.

Teacher's Note:
1. A small value of B does not mean a small share of energy.
2. The factor 1/μ₀ in u_B makes up for the small B.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Welders do use protective goggles, so the Assertion is correct.
2. A welding arc emits strong UV, which can damage the eyes; special glass absorbs much of it. The Reason is correct.
3. The Reason gives the purpose of the goggles, so it explains the Assertion.

Teacher's Note:
1. UV can damage the eyes and skin.
2. Most of the Sun's UV is stopped by the ozone layer, but a welding arc is right in front of the eyes.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. Only accelerated charges radiate EM waves, so the Assertion is correct.
2. A moving charge forms a current and produces a magnetic field, so the Reason is correct.
3. Producing a steady magnetic field does not explain why there is no radiation; the real reason is that the charge is not accelerating. So the Reason is not the correct explanation.

Teacher's Note:
1. Radiation needs fields that change with time, which needs acceleration.
2. Choose (b) when both statements are true but unrelated.

Answer: (d) 0.15 A

Explanation:
1. The displacement current between the plates equals the conduction current in the leads.
2. i_d = i = 0.15 A

Teacher's Note:
1. Zero is the answer only for conduction current in the gap.
2. This equality keeps the current continuous around the circuit.

Answer: (b) 1.875 × 10⁹ V s⁻¹

Explanation:
1. i = C \( \frac{dV}{dt} \), so \( \frac{dV}{dt} = \frac{i}{C} \)
2. \( \frac{dV}{dt} = \frac{0.15}{80 \times 10^{-12}} \) = 1.875 × 10⁹ V s⁻¹

Teacher's Note:
1. 1 pF = 10⁻¹² F; using 10⁻⁹ gives the wrong option 1.875 × 10⁶.
2. A small capacitance charges very quickly.

Answer: (a) 1.7 × 10¹⁰ V m s⁻¹

Explanation:
1. i_d = ε₀ \( \frac{d\Phi_E}{dt} \), so \( \frac{d\Phi_E}{dt} = \frac{i_d}{\varepsilon_0} \)
2. \( \frac{d\Phi_E}{dt} = \frac{0.15}{8.854 \times 10^{-12}} \) ≈ 1.7 × 10¹⁰ V m s⁻¹

Teacher's Note:
1. The unit of electric flux is V m, so its rate of change is in V m s⁻¹.
2. Divide by ε₀, do not multiply by it.

Answer: (c) zero

Explanation:
1. When the capacitor is fully charged, the charge and hence the electric field between the plates stop changing.
2. dΦ_E/dt = 0, so the displacement current is zero.

Teacher's Note:
1. A steady field, however strong, gives no displacement current.
2. This matches the fact that a charged capacitor blocks DC.

Answer: (b) a magnetic field produced by the displacement current

Explanation:
1. In the gap the conduction current is zero, but the changing electric field gives a displacement current.
2. By the Ampere–Maxwell law, this produces a magnetic field around the gap.

Teacher's Note:
1. A changing electric field is a source of magnetic field.
2. This is the reverse of Faraday's law.

Answer: (b) 3.125 m

Explanation:
1. λ = \( \frac{c}{\nu} \) = \( \frac{3 \times 10^8}{96 \times 10^6} \)
2. λ = 3.125 m

Teacher's Note:
1. 1 MHz = 10⁶ Hz.
2. FM waves have wavelengths of a few metres, so they are radio waves.

Answer: (a) 1 × 10⁻⁹ T

Explanation:
1. B₀ = \( \frac{E_0}{c} \) = \( \frac{0.3}{3 \times 10^8} \)
2. B₀ = 1 × 10⁻⁹ T

Teacher's Note:
1. E₀/B₀ = c for every EM wave in vacuum or air.
2. The magnetic field is far smaller than the Earth's field.

Answer: (d) at the same speed

Explanation:
1. All electromagnetic waves travel at the same speed c in vacuum (and very nearly in air), whatever their frequency.
2. The AM wave has a longer wavelength but travels at the same speed.

Teacher's Note:
1. Speed = νλ: a lower frequency means a longer wavelength, not a lower speed.
2. This is true for the whole spectrum, from radio to gamma rays.

Answer: (c) 2.08 m

Explanation:
1. The frequency does not change on entering glass; the speed becomes v = c/n.
2. λ′ = \( \frac{\lambda}{n} \) = \( \frac{3.125}{1.5} \) ≈ 2.08 m

Teacher's Note:
1. Frequency is set by the source and stays the same in every medium.
2. Multiplying by n gives the trap 4.69 m.

Answer: (c) 5 × 10⁻¹⁰ T

Explanation:
1. E and B oscillate in phase, so at every instant B = \( \frac{E}{c} \).
2. B = \( \frac{0.15}{3 \times 10^8} \) = 5 × 10⁻¹⁰ T

Teacher's Note:
1. Because E and B are in phase, when E is half its peak, B is also half its peak.
2. B is never zero when E is not zero.