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An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm^-1. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum :

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$E_{y} = 60 \sin [\frac{π}{4} \times 10^{3} (x - 3 \times 10^{8} t)] \hat{j} {Vm}^{- 1}$

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

$E_{y} = 2 \times 10^{- 7} \sin [\frac{π}{4} \times 10^{4} (x - 4 \times 10^{8} t)] \hat{j} {Vm}^{- 1}$

$B_{z} = 60 \sin [\frac{π}{4} \times 10^{4} (x - 4 \times 10^{8} t)] \hat{k} T$

$E_{y} = 60 \sin [\frac{π}{4} \times 10^{3} (x - 3 \times 10^{8} t)] \hat{j} {Vm}^{- 1}$

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

$E_{y} = 2 \times 10^{- 7} \sin [\frac{π}{4} \times 10^{3} (x - 3 \times 10^{8} t)] \hat{j} {Vm}^{- 1}$

$B_{z} = 60 \sin [\frac{π}{4} \times 10^{3} (x - 3 \times 10^{8} t)] \hat{k} T$

answer is B.

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Detailed Solution

Complete Solution:

k = 2π/λ = π/4 × 10³ m^-1

ω = c × k = 3 × 10⁸ rad/s

B₀ = E₀/c = 2 × 10^-7 T

Electric Field (E_y in the y-direction):

E_y = 60 sin((π/4) × 10³ x - 3 × 10⁸ t) ĵ V/m

Magnetic Field (B_z in the z-direction):

B_z = 2 × 10^-7 sin((π/4) × 10³ x - 3 × 10⁸ t) k̂ T

Final Answer:

E_y = 60 sin((π/4) × 10³ x - 3 × 10⁸ t) ĵ V/m

B_z = 2 × 10^-7 sin((π/4) × 10³ x - 3 × 10⁸ t) k̂ T

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