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The oscillating magnetic field in a plan...

The oscillating magnetic field in a plane electromagnetic wave is given as `B_(Y)=8xx10^(-6)sin (5000 pi x xx-3xx10^(11)pi t)T`.
(a) Frequency
(b) Wavelength
(c) Speed of the wave
(d) Electric field
(e) Write down expression for oscillating electric field.

Text Solution

Verified by Experts

Comparing given equation with standard equation
`B_(gamma) = B_(0) (kx - omegat )`
(a) `omega=3 xx 10^(11) pi`
`2 pi f = 3 xx 10^(11) pi`
`f=1.5 xx 10^(11) Hz`
(b) `k = (2pi)/(lambda)`
`lambda= (2pi)/(5000pi) = 0.4 xx 10^(-3) `m
`lambda = 0.4` mm
(c ) `v = (omega)/(k)`
`= (3xx10^(11) xx pi)/(5000pi)`
`= 0.6 xx 10^(6)`
`=6xx 10^7` m/s
(d) `- (E_0)/(B_0)`
`E_0= v xx B_0`
`= 6 xx 10^7 xx 8 xx 10^(-6)`
`=480 (V)/(m)`
(e) As wave is travelling along the x-axis.
`bar(E) xx bar(B)` should be along x-axis
`- (overset(^)(k) xx overset(^)(j)) = overset(^)(i)`
`E_2 = 480 sin (5000 pi xx -3 xx 10^11 pi t) (V)/(m)`
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