Question

The magnetic field in a plane electromagnetic wave is given by: by = 12 108 sin (1.20 107 z + 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.)