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Electromagnetic theory miscellaneous

Electromagnetic Theory

  1. The expression for B, given that in free space E = 15 cos (6π × 108 t – 2πz) ix V/m is—
    1. 5 × 10–8 cos (6π × 108 t – 2πz) iy
    2. – 90π × 108 sin (6π × 108 t – 2πz) ix
    3. – 45 × 108 sin (6π × 108 t – 2πz) iy
    4. 5 × 10–8 [cos (6π × 108 t – 2πz) iy – sin (6π × 108 t – 2πz) iz]
Correct Option: A

The given wave is travelling in the + z direction (because of the presence of the term – 2 πz) and E is entirely in the x-direction. Now E and H direction gives the direction of travel of tower. It is concluded, therefore, that H must be in + y direction.
ix × iy = iz
Further, we know that

| H | =
|E|
and B = µ0 H
η

η =
µ0
or | B | =
µ0 |E|
ε0µ00

or
B = E/V
= ∵ = V
1
µ00

or
B =
15 cos (6π × 108 t – 2πz) iy
3 × 108

or
B = 5 × 10-8 cos (6π × 108 t – 2π z) iy Wb/m2



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