JEE Main · 2024 · 09 Apr 2024 · Shift 1 · EM Waves

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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 60 Vm

^{- 1}

, the equation for magnetic field is:

(A) $B_{z} = 60 sin [\frac{π}{2} (x - 3 \times 1 0^{8} t)] \hat{k}$ T
(B) $B_{z} = 2 \times 1 0^{- 7} sin [\frac{π}{2} \times 1 0^{3} (x - 3 \times 1 0^{8} t)] \hat{k}$ T✓ Correct
(C) $B_{x} = 60 sin [\frac{π}{2} (x - 3 \times 1 0^{8} t)] \hat{i}$ T
(D) $B_{z} = 2 \times 1 0^{- 7} sin [\frac{π}{2} (x - 3 \times 1 0^{8} t)] \hat{k}$ T

Answer: (B)

Solution

B_{0} = \frac{E _{0}}{c} = \frac{60}{3 \times 1 0 ^{8}} = 2 \times 1 0^{- 7}

k = \frac{2 π}{λ} = \frac{2 π}{4 \times 1 0 ^{- 3}} = \frac{π}{2} \times 1 0^{3}

. Wave along

x

E

along

y

⟹

B

along

z

B_{z} = 2 \times 1 0^{- 7} sin [\frac{π}{2} \times 1 0^{3} (x - 3 \times 1 0^{8} t)] \hat{k}

T. Option (2).

JEE Main · 2024 · 09 Apr 2024 · Shift 1 · Single correct option

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JEE Main · 2024 · 09 Apr 2024 · Shift 1 · EM Waves

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