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The magnetic field in a plane electromag...

The magnetic field in a plane electromagnetic wave is given by `B_(y) = 2xx10^7 T sin (0.5xx10^3x+1.5xx10^11 t) T`
(a) What is the wavelength and frequency of the wave?
(b) Write an expression for the eletric field.

Text Solution

Verified by Experts

(i) Comparing the given equation with the standard equation of electromagnetic wave,
`B = B_(0) sin (kx + omegat)`
We have, `k = (2pi)/(lambda) = 0.5 xx 10^(2)`
`:. Lambda = (2pi)/(0.5 xx 10^(3)) m = 1.26 cm`
`omega = 2piv = 1.5 xx 10^(11)`
`:. v = (1.5 xx 10^(11))/(2pi) Hz = 2.38 xx 10^(10) Hz`
Given, `B_(0) = 2 xx 10^(-7)T`
`:. E_(0) = B_(0)c = 2 xx 10^(-7) xx 3 xx 10^(8) = 60 NC^(-1)`
The electric field is perpendicular to both, the magnitude field and the direaction of propagation of wave, Thus
`E_(z) = (60 NC^(-1))sin (0.5 xx 10^(3) x + 1.5 xx 10^(11)t)`
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