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JEE MAIN 2022
28-06-22
Question
An EM wave propagating in $x$-direction has a wavelength of 8 mm . The electric field vibrating $y$-direction has maximum magnitude of $60 \mathrm{Vm}^{-1}$. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum :
Select the correct option:
A
(A) $\mathrm{E}_{\mathrm{y}}=60 \sin \left[\frac{\pi}{4} \times 10^3\left(\mathrm{x}-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{j}} \mathrm{Vm}^{-1}, \mathrm{~B}_{\mathrm{z}}=2 \sin \left[\frac{\pi}{4} \times 10^3\left(\mathrm{x}-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{k}} \mathrm{T}$
B
$\mathrm{E}_{\mathrm{y}}=60 \sin \left[\frac{\pi}{4} \times 10^3\left(\mathrm{x}-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{j}} \mathrm{Vm}^{-1}, \mathrm{~B}_{\mathrm{z}}=2 \times 10^{-7} \sin \left[\frac{\pi}{4} \times 10^3\left(\mathrm{x}-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{k}} \mathrm{T}$
C
$\mathrm{E}_{\mathrm{y}}=2 \times 10^{-7} \sin \left[\frac{\pi}{4} \times 10^3\left(\mathrm{x}-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{j}} \mathrm{Vm}^{-1}, \mathrm{~B}_{\mathrm{z}}=60 \sin \left[\frac{\pi}{4} \times 10^3\left(\mathrm{x}-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{k}} \mathrm{T}$
D
$\mathrm{E}_{\mathrm{y}}=2 \times 10^{-7} \sin \left[\frac{\pi}{4} \times 10^4\left(\mathrm{x}-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{j}} \mathrm{Vm}^{-1}, \mathrm{~B}_{\mathrm{z}}=60 \sin \left[\frac{\pi}{4} \times 10^4\left(\mathrm{x}-4 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{k}} \mathrm{T}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$$ B_0=\frac{E_0}{C}=\frac{60}{3 \times 10^8}=2 \times 10^{-7} T $$ $\hat{\mathrm{E}} \times \hat{\mathrm{B}}$ must be direction of propagation. So, $\hat{\mathrm{B}} \rightarrow \mathrm{z}$-axis $$ \begin{aligned} & k=\frac{2 \pi}{\lambda}=\frac{\pi}{4} \times 10^3 \mathrm{~m}^{-1} \\ & E_y=60 \sin \left[\frac{\pi}{4} \times 10^3\left(\mathrm{x}-3 \times 10^8 \mathrm{t}\right)\right] \hat{j} V_m^{-1} \\ & E_z=2 \times 10^{-7} \sin \left[\frac{\pi}{4} \times 10^3\left(\mathrm{x}-3 \times 10^8 \mathrm{t}\right)\right] \hat{\mathrm{kT}} \end{aligned} $$
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