The electric field in a plane electromagnetic wave is given by : The expression for magnetic field associated with this electromagnetic wave is ____

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Solution

Q.
The electric field in a plane electromagnetic wave is given by :

$E_{y} = 69 \sin [0.6 \times 10^{3} x - 1.8 \times 10^{11} t] V / m$

The expression for magnetic field associated with this electromagnetic wave is ________ T. [2026]

1 $B_{z} = 2.3 \times 10^{- 7} \sin [0.6 \times 10^{3} x + 1.8 \times 10^{11} t]$

2 $B_{z} = 2.3 \times 10^{- 7} \sin [0.6 \times 10^{3} x - 1.8 \times 10^{11} t]$

3 $B_{y} = 69 \sin [0.6 \times 10^{3} x + 1.8 \times 10^{11} t]$

4 $B_{y} = 2.3 \times 10^{- 7} \sin [0.6 \times 10^{3} x - 1.8 \times 10^{11} t]$

Ans.
(2)

$\hat{B} = \hat{c} \times \hat{E}$

$\Rightarrow \hat{c} = \hat{i} because phase of electric field is function of x .$

$\Rightarrow \hat{E} = \hat{j} (given)$

$\Rightarrow \hat{B} = \hat{i} \times \hat{j} = \hat{k}$

$| B |$ $= \frac{| E |}{c} = \frac{69 \times 0.6 \times 10^{3}}{1.8 \times 10^{11}} = \frac{69}{3 \times 10^{8}}$

$| B |$ $= 2.9 \times 10^{- 7}$

$\vec{B_{2}} = 2.9 \times 10^{- 7} \sin (0.6 \times 10^{3} x - 1.8 \times 10^{11} t)$

(phase is same as that of electric field)

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