NCERT Physics Class 12 Exemplar Ch 8 Electromagnetic Waves Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Q 32 A plane EM wave travelling along z direction is described by Show that

(i) The average energy density of the wave is given by

.

(ii) The time averaged intensity of the wave is given by

EM Wave Travelling Along Z Direction
  1. E-field contributation is

B-field contributation is

Total energy density (1)

  • The values of and vary from point to point and from moment to moment. Hence, the effective values of and are their time averages.

  • The graph of and are identical in shape but shifted by , so the average values of and are also equal over any integral multiple of π.

And also

So by symmetry the average of = average of

Substuting in Equation (1) ,

(2)

(b) We know

Therefore,