If the magnetic field in a plane electromagnetic wave is given by $\vec{B} = 3 \times 10^{- 8} \sin (1.6 \times 10^{3} x + 48 \times 10^{10} t) \hat{j} T;$ then what will be the expression for the electric field?

Easy

A

$\vec{E} = (9 \sin (1.6 \times 10^{3} x + 48 \times 10^{10} t) \hat{k} V / m)$
B

$\vec{E} = (3 \times 10^{- 8} \sin (1.6 \times 10^{3} x + 48 \times 10^{10} t) \hat{i} V / m)$
C

$\vec{E} = (3 \times 10^{- 8} \sin (1.6 \times 10^{3} x + 48 \times 10^{10} t) \hat{j} V / m)$
D

$\vec{E} = (60 \sin (1.6 \times 10^{3} x + 48 \times 10^{10} t) \hat{k} V / m)$

Solution

$\begin{array}{l} W e k n o w t h a t, \frac{E_{0}}{B_{0}} = C (s p e e d o f l i g h t i n v a c u u m) \\ A m p l i t u d e o f e l e c t r i c f i e l d, E_{0} = B_{0} C = 3 \times 10^{- 8} \times 3 \times 10^{8} = 9 N / C \\ O n l y o p t i o n (1) m a t c h e s . \end{array}$
when an electro magnetic wave passes through a medium electric field vector ,magnetic field vector and direction of propagation of the wave are in mutually perpendicular directions.
$E = E_{0} \sin [\begin{matrix} k x + ω t \end{matrix}]$

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