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.