Vidaara.orgClass 12 · Physics
CodeVID-P12-04-NPW-01
Nature & Properties of EM Waves — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
Electromagnetic waves are:
- A.longitudinal
- B.transverse
- C.neither
- D.sometimes longitudinal
2.
The direction of propagation of an EM wave is along:
- A.$\vec{E}$
- B.$\vec{B}$
- C.$\vec{E}\times\vec{B}$
- D.$\vec{B}-\vec{E}$
3.
In vacuum the ratio $\frac{E_0}{B_0}$ equals:
- A.$\mu_0$
- B.$c$
- C.$\epsilon_0$
- D.$\frac{1}{c}$
4.
In an EM wave the electric and magnetic energy densities are:
- A.equal
- B.$u_E=2u_B$
- C.$u_B=2u_E$
- D.unrelated
5.
EM waves carry momentum related to energy by:
- A.$p=Uc$
- B.$p=\frac{U}{c}$
- C.$p=\frac{U}{c^2}$
- D.$p=Uc^2$
Section B — Short Answer (2 marks)
3 × 2 = 6 marks
6.
An EM wave has $E_0=90\ \text{V/m}$. Find $B_0$.
7.
Why is the electric field, rather than the magnetic field, mainly responsible for the optical effects of light?
8.
State two properties unique to EM waves compared with sound.
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
9.
An EM wave has $E_0=60\ \text{V/m}$. Find its intensity ($\epsilon_0=8.85\times10^{-12}$, $c=3\times10^{8}$).
10.
A laser delivers $5\ \text{W}$ on a $1\ \text{cm}^2$ absorbing spot. Find the radiation pressure ($c=3\times10^{8}$).
Section D — Long Answer (5 marks)
1 × 5 = 5 marks
11.
Describe the structure of a plane EM wave travelling along the x-axis. State the relations for its speed in vacuum, the ratio of field amplitudes, and show that the electric and magnetic energy densities are equal.
Answer Key
Section A — Multiple Choice Questions
- (B) transverse
- (C) $\vec{E}\times\vec{B}$
- (B) $c$
- (A) equal
- (B) $p=\frac{U}{c}$
Section B — Short Answer (2 marks)
- $B_0=\frac{E_0}{c}=\frac{90}{3\times10^{8}}=3\times10^{-7}\ \text{T}$.
- Because $\frac{E_0}{B_0}=c$ is large, $E_0\gg B_0$ numerically, so the electric force on charges in a detector dominates.
- EM waves can travel through a vacuum and can be polarised (being transverse); sound needs a medium and is longitudinal so cannot be polarised.
Section C — Short Answer (3 marks)
- $I=\frac{1}{2}\epsilon_0 E_0^2 c=\frac{1}{2}\times8.85\times10^{-12}\times3600\times3\times10^{8}\approx4.78\ \text{W/m}^2$.
- Intensity $I=\frac{5}{1\times10^{-4}}=5\times10^{4}\ \text{W/m}^2$; $P=\frac{I}{c}=\frac{5\times10^{4}}{3\times10^{8}}\approx1.67\times10^{-4}\ \text{Pa}$.
Section D — Long Answer (5 marks)
- Fields oscillate in phase: $E_y=E_0\sin(kx-\omega t)$, $B_z=B_0\sin(kx-\omega t)$, mutually perpendicular and transverse. Speed $c=\frac{1}{\sqrt{\mu_0\epsilon_0}}$. Ratio $\frac{E_0}{B_0}=c$. Energy densities: $u_E=\frac{1}{2}\epsilon_0 E^2$ and $u_B=\frac{B^2}{2\mu_0}$; using $E=cB$ and $c^2=\frac{1}{\mu_0\epsilon_0}$ gives $u_E=u_B$.
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