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The magnetic field in a plane em wave is given by : By = 12× 10−8 sin (1.20× 107Z + 3.60 × 1015t) Tesla. Calculate the : (i) energy density associated with the em wave (ii) speed of the wave |
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Answer» (i) Here, B0 =12× 10−8 Tesla E0 = cB0 = 3× 10−8 × 12 × 10−8 = 36 V/m Average energy density of electric field, uE = \(\frac{1}{4}\)∈0\(E^2_0\) = \(\frac{1}{4}\) \(\times\) 8.85 × 10−12 × 36 × 36 = 2867.4 × 10−12 = 2.87× 10−9 J/m3 Average energy density of magnetic field, uB = uE ∴ Energy density associated with the em wave. u = uE+ uB = 2uE = 2× 2.87 × 10−9 = 5.74 × 10−9 J/m3 (ii) \(\frac{1}{c}\) = \(\frac{k}{ω}\) or c = \(\frac{ω}{k}\) = \(\frac{3.6\times 10^{15}}{1.2\times 10^7}\) = 3 × 108 m/s |
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