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

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  1. E= 60 V/m sin (8π × 102z + 6π × 1011t)
  2. Ey = 6 V/m sin (8π × 102z + 6π × 1011t)
  3. Ex = 60 V/m sin (8π × 102z + 6π × 1011t)
  4. Ex = 6 V/m sin (8π × 102z + 6π × 1011t)

Answer (Detailed Solution Below)

Option 3 : Ex = 60 V/m sin (8π × 102z + 6π × 1011t)
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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 

E= 60 V/m

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

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