A plane EM wave is propagating along direction. It has wavelength of 4 mm. If electric field is in direction with the maximum magnitude of 6O , the equation for magnetic field is

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Solution

Q.
A plane EM wave is propagating along $x$ direction. It has a wavelength of 4 mm. If electric field is in $y$ direction with the maximum magnitude of 6O $V m^{- 1}$ , the equation for magnetic field is [2024]

1 $B_{z} = 60 \sin [\frac{π}{2} (x - 3 \times 10^{8} t)] \hat{k} T$

2 $B_{z} = 2 \times 10^{- 7} \sin [\frac{π}{2} \times 10^{3} (x - 3 \times 10^{8} t)] \hat{k} T$

3 $B_{x} = 60 \sin [\frac{π}{2} (x - 3 \times 10^{8} t)] \hat{i} T$

4 $B_{z} = 2 \times 10^{- 7} \sin [\frac{π}{2} (x - 3 \times 10^{8} t)] \hat{k} T$

Ans.
(2)

$λ = 4 m m = 4 \times 10^{- 3} m$

$K = \frac{2 π}{4 \times 10^{- 3}} = \frac{π}{2} \times 10^{3} \cdot m^{- 1}$

$ω = v \times K = 3 \times 10^{8} \times \frac{π}{2} \times 10^{3} = \frac{3 π}{2} \times 10^{11} r a d / s$

Electric field $\Rightarrow y$ direction

Propagation field $\Rightarrow x$ direction

Mgnetic field $\Rightarrow z$ direction

$\hat{E} \times \hat{B} = \hat{c}$ and $B_{0} = \frac{E_{0}}{c} = 2 \times 10^{- 7} T$

$B_{z} = 2 \times 10^{- 7} \sin [\frac{π}{2} \times 10^{3} (x - 3 \times 10^{8} t)] \hat{k} T$

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