Question

Electric field in a plane electromagnetic wave is given by
$E=50\sin (500x-10\times {10}^{10}t)\text{V/m}$.
The velocity of electromagnetic wave in this medium is :
(Given $c=$ speed of light in vacuum)

• A. $c$
• B. $\frac{2}{3}c$
• C. $\frac{3}{2}c$
• D. $\frac{c}{2}$

Answer 1

The correct option is B $\frac{2}{3}c$

Given :-
$E=50\sin (500x-10\times {10}^{10}t)\text{V/m}$
From the given equation we can say that :
$\omega ={10}^{11}\text{rad/s}$
$k=500\text{m}$
The speed of the electromagnetic wave is given by :
$v=\frac{\omega }{k}=\frac{{10}^{11}}{500}=2\times {10}^8\text{m/s}$
Or, $v=\frac{2c}{3}$