In
a plane electromagnetic wave, the electric field oscillates
sinusoidally at a frequency of 2.0 × 10^{10}
Hz and amplitude 48 V m^{−1}.

**(a)** What
is the wavelength of the wave?

**(b)
** What is the amplitude of the
oscillating magnetic field?

**(c) ** Show
that the average energy density of the **E
**field equals the average energy
density of the **B **field.
[*c *=
3 × 10^{8}
m s^{−1}.]

Frequency of the
electromagnetic wave, *ν*
= 2.0 × 10^{10} Hz

Electric field
amplitude, *E*_{0} = 48 V m^{−1}

Speed of light, *c*
= 3 × 10^{8} m/s

**(a)** Wavelength
of a wave is given as:

**(b)** Magnetic
field strength is given as:

**(c)** Energy
density of the electric field is given as:

And, energy density of the magnetic field is given as:

Where,

∈_{0}
= Permittivity of free space

μ_{0}
= Permeability of free space

We
have the relation connecting *E* and *B* as:

*E*
= *cB* … (1)

Where,

… (2)

Putting equation (2) in equation (1), we get

Squaring both sides, we get

**
**