8.Electromagnetic waves
medium

For a plane electromagnetic wave, the magnetic field at a point $x$ and time $t$ is

$\overrightarrow{ B }( x , t )=\left[1.2 \times 10^{-7} \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ k }\right] T$

The instantaneous electric field $\overrightarrow{ E }$ corresponding to $\overrightarrow{ B }$ is : (speed of light $\left.c=3 \times 10^{8} ms ^{-1}\right)$

A

$\overrightarrow{ E }( x , t )=\left[36 \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ k }\right] \frac{ v }{ m }$

B

$\overrightarrow{ E }( x , t )=\left[-36 \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ j }\right] \frac{ v }{ m }$

C

$\overrightarrow{ E }( x , t )=\left[-36 \sin \left(1 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ j }\right] \frac{ v }{ m }$

D

$\overrightarrow{ E }( x , t )=\left[36 \sin \left(1 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ j }\right] \frac{ v }{ m }$

(JEE MAIN-2020)

Solution

$\overrightarrow{ E }$ and $\overrightarrow{ B }$ are perpendicular for $EM$ wave

$E _{0}= CB _{0}$

$=3 \times 10^{8} \times 1.2 \times 10^{-7}$

$=36$

Having same phase

Propagation is along $-x-$axis, $\overrightarrow{ B }$ is along $z-$axis

hence $\overrightarrow{ E }$ must be along $y-$axis.

Standard 12
Physics

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