Board Previous Year Questions

How to Use This Section

CBSE Board-pattern questions on Electromagnetic Waves by mark value, with examiner-rewarded model answers. The Board regulars: displacement current (definition + the capacitor argument), the Ampere-Maxwell law, properties of EM waves, the E-B-propagation geometry, $B_0 = E_0/c$ numericals, and spectrum bands with production/detection/uses — this chapter is the highest marks-per-revision-hour in the book.

1-Mark Questions (Definitions & Direct)

Q1. Define displacement current. Answer: The current equivalent of a time-varying electric flux, $i_d = \varepsilon_0\,d\Phi_E/dt$, which produces a magnetic field exactly as a conduction current does.

Q2. Write the Ampere-Maxwell law. Answer: $\oint\vec{B}\cdot d\vec{l} = \mu_0 i_c + \mu_0\varepsilon_0\dfrac{d\Phi_E}{dt}$ — circulation of B is sourced by conduction plus displacement current.

Q3. What is the ratio $E_0/B_0$ in an electromagnetic wave? Answer: $E_0/B_0 = c$, the speed of light in vacuum ($3\times10^8$ m/s).

Q4. Name the EM radiation used to kill germs in water purifiers. Answer: Ultraviolet rays.

Q5. Which part of the EM spectrum is absorbed by the ozone layer? Answer: Ultraviolet radiation from the sun (ozone layer at about 40-50 km altitude).

Q6. Name the EM waves produced by radioactive nuclei and state one use. Answer: Gamma rays; used in medicine to destroy cancer cells.

2-Mark Questions (Short Answer)

Q7. Why was Ampere's circuital law modified? State the inconsistency. Answer: For a charging capacitor, a flat surface spanning an Amperian loop is pierced by the wire (giving $B(2\pi r) = \mu_0 i$) while a pot-shaped surface through the gap encloses no conduction current (giving B = 0) — the same point gets two different fields. Maxwell added the displacement current $\varepsilon_0\,d\Phi_E/dt$, which flows exactly where the wire does not, so every surface now yields the same total current.

Q8. List four properties of electromagnetic waves. Answer: (i) Transverse — $\vec E \perp \vec B \perp$ propagation ($\hat E\times\hat B$ along $\vec k$); (ii) travel at $c = 1/\sqrt{\mu_0\varepsilon_0}$ in vacuum, needing no medium; (iii) E and B oscillate in phase with $B_0 = E_0/c$; (iv) carry energy (and momentum) from place to place.

Q9. An EM wave travels along +z with E along x. Give the direction of B and the expressions for both fields. Answer: B is along y ($\hat i\times\hat j = \hat k$). $E_x = E_0\sin(kz-\omega t)$, $B_y = B_0\sin(kz-\omega t)$ with $B_0 = E_0/c$.

Q10. Why are microwaves suitable for radar, and what tunes a microwave oven to food? Answer: Their short (cm) wavelengths form narrow, well-directed beams — ideal for locating aircraft and timing vehicles. Ovens select the frequency to match the resonant frequency of water molecules, transferring wave energy efficiently into molecular kinetic energy.

Q11. Distinguish X-rays from gamma rays in origin, given that their wavelength ranges overlap. Answer: X-rays arise from atomic processes — typically high-energy electrons decelerating at a metal target; gamma rays arise from nuclear processes — nuclear reactions and radioactive decay. Production, not wavelength, is the classifier.

3-Mark Questions (Application & Numericals)

Q12. A parallel-plate capacitor is charged by a 0.5 A current. Find (i) the displacement current between the plates, (ii) the rate of change of electric flux. Answer: (i) $i_d = i = 0.5$ A (continuity). (ii) $d\Phi_E/dt = i_d/\varepsilon_0 = 0.5/8.85\times10^{-12} = 5.6\times10^{10}$ V m s$^{-1}$.

Q13. The electric field of a plane EM wave is $E = 120\sin(kz - \omega t)\,\hat{i}$ V/m at 50 MHz. Find $B_0$, k and $\omega$, and write $\vec{B}$. Answer: $B_0 = E_0/c = 4\times10^{-7}$ T; $\omega = 2\pi\nu = 3.14\times10^8$ rad/s; $k = \omega/c = 1.05$ rad/m; $\vec{B} = 4\times10^{-7}\sin(1.05z - 3.14\times10^8 t)\,\hat{j}$ T.

Q14. Write Maxwell's four equations and state what each expresses. Answer: $\oint\vec E\cdot d\vec A = Q/\varepsilon_0$ (charges source E); $\oint\vec B\cdot d\vec A = 0$ (no monopoles); $\oint\vec E\cdot d\vec l = -d\Phi_B/dt$ (changing B makes E); $\oint\vec B\cdot d\vec l = \mu_0 i_c + \mu_0\varepsilon_0\,d\Phi_E/dt$ (currents and changing E make B).

Q15. Name the EM radiation for each: (i) maintaining the earth's warmth via the greenhouse effect, (ii) treating cancer, (iii) aircraft navigation, (iv) photographing in fog/night from satellites (heat signatures), (v) sterilising water, (vi) broadcasting. Answer: (i) Infrared; (ii) gamma rays (also X-rays for certain cancers); (iii) microwaves (radar); (iv) infrared; (v) ultraviolet; (vi) radio waves.

5-Mark Questions (Long Answer)

Q16. (a) Explain, with the charging-capacitor argument, the need for displacement current and state the Ampere-Maxwell law. (b) Show that the displacement current between the plates equals the conduction current in the leads. (c) A 100 pF capacitor is connected to $V = 230\sin(300t)$ V; find the peak displacement current. Answer:

1. (a) Two surfaces with the same boundary give different enclosed conduction currents (wire-pierced disc vs gap-passing pot surface) — Ampere's law contradicts itself. Maxwell's repair: a changing electric flux acts as the displacement current $i_d = \varepsilon_0\,d\Phi_E/dt$, giving $\oint\vec B\cdot d\vec l = \mu_0 i_c + \mu_0\varepsilon_0\,d\Phi_E/dt$.
2. (b) Between plates of area A, $E = Q/(A\varepsilon_0)$, so $\Phi_E = Q/\varepsilon_0$ and $i_d = \varepsilon_0\,d\Phi_E/dt = dQ/dt = i$ — exactly the charging current.
3. (c) $i_d^{max} = CV_0\omega = 100\times10^{-12}\times230\times300 = 6.9\times10^{-6}$ A $= 6.9\ \mu$A.

Q17. (a) Describe the nature of electromagnetic waves (geometry, speed, phase, medium). (b) Derive nothing but state the meaning of $c = 1/\sqrt{\mu_0\varepsilon_0}$ and $v = 1/\sqrt{\mu\varepsilon}$. (c) The magnetic field of a wave is $B_y = 2\times10^{-7}\sin(0.5\times10^3x + 1.5\times10^{11}t)$ T; find the wavelength, frequency and the electric field. Answer:

1. (a) Transverse waves: E, B and propagation mutually perpendicular, $\hat E\times\hat B$ along propagation; E and B in phase with $B_0 = E_0/c$; self-sustaining field oscillations needing no medium; speed in vacuum the same for all wavelengths.
2. (b) The vacuum speed is fixed by the electric and magnetic constants ($3\times10^8$ m/s — light's measured speed, identifying light as an EM wave); in a medium, $\mu$ and $\varepsilon$ replace $\mu_0, \varepsilon_0$, so the speed (and hence refractive index $n = \sqrt{\mu_r\varepsilon_r}$) depends on the medium.
3. (c) $\lambda = 2\pi/k = 2\pi/500 = 1.26$ cm; $\nu = \omega/2\pi = 23.9$ GHz; $E_0 = cB_0 = 60$ V/m, directed along z (so that $\hat E\times\hat B$ points along $-x$, the propagation direction): $E_z = 60\sin(0.5\times10^3x + 1.5\times10^{11}t)$ V/m.