MCQ
A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}},$ with its polarization along the direction $\hat{\mathrm{k}}$. The correct form of the magnetic field of the wave would be (here $\mathrm{B}_{0}$ is an appropriate constant)
  • $\mathrm{B}_{0} \frac{\hat{\mathrm{i}}-\hat{\mathrm{j}}}{\sqrt{2}} \cos \left(\omega \mathrm{t}-\mathrm{k} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}\right)$
  • B
    $\mathrm{B}_{0} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}} \cos \left(\omega \mathrm{t}-\mathrm{k} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}\right)$
  • C
    $\mathrm{B}_{0} \hat{\mathrm{k}} \cos \left(\omega \mathrm{t}-\mathrm{k} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}\right)$
  • D
    $\mathrm{B}_{0} \frac{\hat{\mathrm{j}}-\hat{\mathrm{i}}}{\sqrt{2}} \cos \left(\omega \mathrm{t}+\mathrm{k} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}\right)$

Answer

Correct option: A.
$\mathrm{B}_{0} \frac{\hat{\mathrm{i}}-\hat{\mathrm{j}}}{\sqrt{2}} \cos \left(\omega \mathrm{t}-\mathrm{k} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}\right)$
a
Direction of polarisation $=\hat{\mathrm{E}}=\hat{\mathrm{k}}$

Direction of propagation $=\hat{\mathrm{E}} \times \hat{\mathrm{B}}=\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}$

$\therefore \hat{\mathrm{E}} \times \hat{\mathrm{B}}=\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}}$

$\hat{\mathrm{B}}=\frac{\hat{\mathrm{i}}-\hat{\mathrm{j}}}{\sqrt{2}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Let r be the distance of a point on the axis of a magnetic dipole from its centre. The magnetic field at such a point is proportional to:
Match List-$I$ with List-$II$ :-

List-$I$ $EM-Wave$

List-$II$ $Wavelength$ $Range$

$(A)$ infra-red $(i)$ $<10^{-3} \mathrm{~nm}$
$(B)$ Ultraviolet $(II)$ $400 \mathrm{~nm}$ to $1 \mathrm{~nm}$
$(C)$X-rays $(iii)$ $1 \mathrm{~mm}$ to $700 \mathrm{~nm}$
$(D)$ Gamma rays $(iv)$ $1 \mathrm{~nm}$ to $10^{-3} \mathrm{~nm}$

Choose the correct answer from the options given below:

An alternating supply of $220\,V$ is applied across a circuit with resistance $22\,\Omega $ and impedance $44\,\Omega $. The power dissipated in the circuit is.........$W$
A charge $+ Q$ is moving upwards vertically. It enters a magnetic field directed to the north. The force on the charge will be towards
Electrons with energy 80 keV are incident on the tungsten target of an X-ray tube. K shell electrons of tungsten have ionization energy 72.5 keV. X-rays emitted by the tube contain only
An e.m.f. of 12 volts is induced in a given coil when the current in it changes at the rate of 48 amperes per minute. The self inductance of the coil is
A person A can clearly see objects between 25cm and 200cm. Which of the following may represent the range of clear vision for a person B having muscles stronger than A, but all other parameters of eye identical to that of A?
A radioactive nucleus is being produced at a constant rate a per second. Its decay constant is l. If $\mathrm{N}_0$ are the number of nuclei at time t = 0, then maximum number of nuclei possible are
The half life of the isotope $11^{\mathrm{Na}^{24}}$ is 15 hrs. How much time does it take for $\frac{7}{8} \mathrm{th}$ of a sample of this isotope to decay
A steady current is set up in a cubic network composed of wires of equal resistance and length $d$ as shown in figure. What is the magnetic field at the centre P due to the cubic network