The magnetic field of a plane electromagnetic wave is given by B= 2 × 10-7 sin (0.6 × 103y + 2 × 1011t) T. An expression for its electric field is :

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CUET Physics 18th Aug 2022 Official Paper
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  1. Ex = 2 × 10-7 sin (0.6 × 103y + 2 × 1011t) V/M
  2. Ey = 60 sin (0.6 × 103y + 2 × 1011t) V/M
  3. Ez = 2 × 10-7 sin (0.6 × 103y + 2 × 1011t) V/M
  4. Ez = 60 sin (0.6 × 103y + 2 × 1011t) V/M

Answer (Detailed Solution Below)

Option 4 : Ez = 60 sin (0.6 × 103y + 2 × 1011t) V/M
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Detailed Solution

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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, B= 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 

E= 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)

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