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Suppose that the electric field amplitud...

Suppose that the electric field amplitude of an electromagnetic wave is `E_(0)=120 N//C` and that its frequency is f=50 MHz. Find expression for B.

A

`4 xx 10^(-7) sin (1.05 x-3.14 xx 10^(8) t) hatk (T)`

B

`4 xx 10^(-7) sin (3.142 x-3.14 xx 10^(8) t) hatk (T)`

C

`4 xx 10^(-7) sin (1.05 x-1.05 xx 10^(8) t) hatk (T)`

D

`4 xx 10^(-7) sin (-3.14 xx 10^(8) t) hatk (T)`

Text Solution

Verified by Experts

The correct Answer is:
A
`C=E_(0)/B_(0) therefore B_(0)=E_(0)/C=(120)/(3 xx 10^(8))=4 xx 10^(-7)T`
`E_(0)K=B_(0) omega, K=B_(0)/E_(0) omega=omega/C=(2pi v)/(C )=(2 xx 3.14 xx 50 xx 10^(6))/(3 xx 10^(8))=1.05m^(-1)`
`lambda=C/f=(3 xx 10^(8))/(50 xx 10^(6))=6m`
`omega=2pif=2 xx 3.14 xx 50 xx 10^(6) =3.14 xx 10^(8)" rad s"^(-1)`
Equation of B is `B_(z)=B_(0) sin (kx-omegat) hatk=4 xx 10^(-7) sin (1.05 x-3.14 x xx 10^(8) t) hatk (T)`
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