The magnetic field in a plane electromagnetic wave is given by B_y  = 0.2 μ T sin (8π × 10²z + 6π × 10¹¹t). Then the electric field of the wave 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, By  = 0.2 μ T sin (8π × 102z + 6π × 1011t)

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 = 0.2 ×10^-6 ×  3 ×10⁸ 

E0 = 60 V/m

So, the electric field in a plane electromagnetic wave is E_x  = 60 V/m sin (8π × 102z + 6π × 1011t)