NCERT Physics Class 12 Exemplar Ch 8 Electromagnetic Waves Part 6

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

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,