Question

The electric field in a plane electromagnetic wave is given by E_z = 60 cos(5x + 1.5 × 10⁹ t) V/m. Then expression for the corresponding magnetic fields is (here subscripts denote the direction of the field) ______.

विकल्प

• By = 2 × 10⁻⁷ cos(5x + 1.5 × 10⁹ t) T

• B_x = 2 × 10⁻⁷ cos(5x + 1.5 × 10⁹ t) T

• B_z = 60 cos(5x + 1.5 × 10⁹ t) T

• B_y = 60 cos(5x + 1.5 × 10⁹ t) T

Answer 1

The electric field in a plane electromagnetic wave is given by E_z = 60 cos(5x + 1.5 × 10⁹ t) V/m. Then expression for the corresponding magnetic fields is (here subscripts denote the direction of the field) B_y = 2 × 10⁻⁷ cos(5x + 1.5 × 10⁹ t) T.

Explanation:

Given: E_z = 60 cos(5x + 1.5 × 10⁹ t) V/m

In an e.m. wave, the phase of the oscillating electric and magnetic fields is the same.

`(E_0)/c = 60/(3 xx 10^8)`

= 2 × 10⁻⁷ T

We see that the wave propagates in the -X direction.

The directions of `vecE, vecB and vecc` are related as

`vecE xx vecB = vecc`

`hatk xx hatj = -hati`

∴ `vecB` is along the Y-direction as `hatk xx hatj = -hati`

∴ B_y = 2 × 10⁻⁷ cos(5x + 1.5 × 10⁹ t) T