Q.

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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a

Ey=60sinπ4×103x3×108tj^Vm1

Bz=2×107sinπ4×103x3×108tk^T

b

Ey=2×107sinπ4×104x4×108tj^Vm1

Bz=60sinπ4×104x4×108tk^T

c

Ey=60sinπ4×103x3×108tj^Vm1

Bz=2sinπ4×103x3×108tk^T

d

Ey=2×107sinπ4×103x3×108tj^Vm1

Bz=60sinπ4×103x3×108tk^T

answer is B.

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Detailed Solution

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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 (Ey in the y-direction):

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

Magnetic Field (Bz in the z-direction):

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

Final Answer:

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

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

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