The magnetic field in a plane electromagnetic wave is given by: B y = 12 × 10 –8 sin (1.20 × 10 7 z + 3.60 × 10 15 t) T. Calculate the (i) Energy density associated with the Electromagnetic wave (ii) Speed of the wave
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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
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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.)