A magnetic field in a plane e.m. wave is given by, `B_y=3xx10^-7 sin[(1.5rad//m)x+(5xx10^8rad//s)t]tesla.`
(a) What is the wavelength and frequency of the wave? (b) Write down an expression for the electric field. (x is the metre and t is in second).

Answer

(a) 4.19m ; `7.95xx10^7Hz (b) E_z=90 sin (1.5x+5xx10^8t)V//m`

Explanation

(a) Comparing the given relation with the
equation of
`B=B_0sin((2pi)/lambdax+(2pit)/T)`
`=B_0sin((2pi)/lambdax+2pitv)`
we have, `B_0=3xx10^-7T`,
`(2pi)/lambda=1.5 or lambda=(2pi)/1.5 =4.19m`
`2piv=5xx10^8 or v=(5xx10^8)/(2pi)=7.95xx10^7Hz`
(b) `E_0=cB_0=(3xx10^8)xx(3xx10^-7)=90V//m`
`E_z=E_0sin((2pix)/lambda+(2pit)/T)`
or `E_z=90sin(1.5x+5xx10^8t)V//m`