The magnetic field of a plane electromagnetic wave is given by B_x = 2 × 10^-7 sin (0.6 × 10³y + 2 × 10^11t) T. An expression for its electric field is :

Concept:

• Electromagnetic wave: It can also be said that electromagnetic waves are the composition of oscillating electric and magnetic fields.
• Electromagnetic waves are shown by a sinusoidal graph.
• It consists of time-varying electric and magnetic fields which are perpendicular to each other and are also perpendicular to the direction of propagation of waves.

• If the electric field oscillated in the x-axis, then the magnetic field will oscillate in the y-axis and the direction of propagation of the electromagnetic wave is in the z-axis.
• The speed of electromagnetic waves equals the speed of light in air.
• The relation between the magnitude of the electric field and the magnetic field is given as E0 = B0 c

Explanation:

Given,

The magnetic field in a plane electromagnetic wave, Bx = 2 × 10-7 sin (0.6 × 103y + 2 × 1011t) T.

Take, the speed of light, c = 3 ×108 ms-1

The relation between the magnitude of the electric field and the magnetic field is given as E0 = B0 c

E0 = 2 ×10-7 ×  3 ×108 

E0 = 60 V/m

So, the electric field in a plane electromagnetic wave is Ez = 60 sin (0.6 × 103y + 2 × 1011t) V/M.

The correct answer is option (4)