A plane electromagnetic wave propagating in the x-direction has a wavelength of 5.0 mm. The electric field is in the y-direction and its maximum magnitude is `30V (m^-1)`. Write suitable equations for the electric and magnetic fields as a function of x and t.

Explanation

Solution:
The equation for the electric and the magnetic fields in
the wave may be written as
`E= (E_0)sin omega(t-(x/c))`
` B=(B_0)sin omega(t-(x/c))`
We have,
`omega = (2 pi v)=(2pi/lambda) c.`
` Thus E=(E_0) sin[2pi/lambda(ct-x)]`
` =(30 V m^-1) sin[(2pi/5.0 mm)(ct-x)].`
` The maximum magnetic field is`
`(B_0)=(E_0)/c = (30V(m^-1)/ 3 xx (10^8)m(s^-1))= (10^-7)T. `
` So, B = B_0 sin[(2pi/ lambda )(ct-x)]`
`=(10^-7)T sin [(2pi/5.0 mm )(ct-x)].`
` The magnetic field is along the z-axis.`