Question

If the magnetic field of a plane electromagnetic wave is given by (The speed of light $ = 3 \times {10^8}m/s $ ) $ B = 100 \times {10^{ - 6}}sin\left[ {2\pi \times 2 \times {{10}^{15}}\left( {t - \dfrac{x}{c}} \right)} \right] $ then the maximum electric field associated with it is:
(A) $ 4 \times {10^4}N/C $
(B) $ 4.5 \times {10^4}N/C $
(C) $ 6 \times {10^4}N/C $
(D) $ 3 \times {10^4}N/C $

Answer 1

Hint To find the maximum electric field associated with it, we need to use the relation between the electric field and the magnetic field of a plane electromagnetic wave which is $ {E_o} = {B_o}c $ .
We need to substitute the values in the equation to find the answer.

Formula used $ {E_o} = {B_o}c $
Where, $ E_0 $ is the magnitude of the electric field, $ B_0 $ is the magnitude of the magnetic field and $ c $ is the speed of light.

Complete step by step answer
Let us consider E0 is the magnitude of the electric field, B0 is the magnitude of the magnetic field and c is the speed of light.
Now, the relation comes as,
 $\Rightarrow {E_o} = {B_o}c $
It is given in the question in the question that,
 $\Rightarrow {B_0} = 100 \times {10^{ - 6}}T $ And $ c = 3 \times {10^8}m/s $
So when we substitute the values in the formula we get,
 $\Rightarrow {E_0} = 100 \times {10^{ - 6}} \times 3 \times {10^8} $
Now on calculating we get,
 $\Rightarrow {E_0} = 3 \times {10^{ - 4}}N/C $
Hence, the correct answer is option (D).

Note
The applications of electromagnetic waves includes,
-Radio waves are used for communication such as television and radio.
-Microwaves are used for cooking food and for satellite communications.
-Infrared light is used by electrical heaters, cookers for cooking food, and by infrared cameras which detect people in the dark.
-Visible light is the light we can see. It is used in fibre optic communications, where coded pulses of light travel through glass fibres from a source to a receiver.