Question

7. The magnetic field in a plane electromagnetic wave is given by:By = 12 × 10–8sin (1.20 × 107z + 3.60 × 1015 t) T. Calculate the(i) Energy density associated with the Electromagnetic wave(ii) Speed of the wave

Answer 1

a)  By = 12 x 10-8 sin [1.20 x 107 z + 3.60 x 1015t]

Now Bo = 12 x 10-8 T and c = 3 x 10 8 m/s

Since Eo =  Bo c = 12 x 10-8 x 3 x 10 8 = 36 V/m

Energy Density = (1/2) ε0Eo2 = (1/2)(8.85 x 10-12) (36x36)

Energy Density = 5.74 x 10-15 J/m3

  b)

By = 12 x 10-8 sin [1.20 x 107 z + 3.60 x 1015t]

Now k= 1.2 x 107 and w = 3.6 x 1015

Since, λ = (2π / k) and f = (w / 2π)

V = λ x f = kw = 3 x 108 m/s (approx.)