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.

Explanation

(a) `B_(y) = 2xx10^(-7) sin (0.5xx10^(3) x+1.5 xx 10^(11)t)T`
`B = B_(0)sin(kx + omegat)`
`B_(0) = 2xx10^(-7)T`
`k = (2pi)/(lambda) = 0.5 xx 10^(3)`
`lambda = (2pi)/(0.5 xx 10^(3))`
`= 4pi xx 10^(-3)m = 4pimm`
`omega = 2pi upsilon = 1.5 xx 10^(11)`
`upsilon = (1.5 xx 10^(11))/(2pi) Hz`
(b) `E_(0) = cB_(0) = 3xx10^(8) xx2xx10^(-7) = 60V//m`
`E =E_(0) sin (kx + omegat)`
`= 60sin(0.5 xx 10^(3) x + 1.5 xx 10^(11)t)V//m`