Suppose
that the electric field part of an electromagnetic wave in vacuum is
**E **=
{(3.1 N/C) cos [(1.8 rad/m) *y *+
(5.4 × 10^{6}
rad/s)*t*]}
.

**(a)
** What is the direction of
propagation?

**(b)
** What is the wavelength λ?

**(c)
** What is the frequency *ν*?

**(d)
** What is the amplitude of the
magnetic field part of the wave?

**(e)
** Write an expression for the
magnetic field part of the wave.

**(a)** From the given electric field vector, it can be inferred
that the electric field is directed along the negative *x*
direction. Hence, the direction of motion is along the negative *y
*direction i.e.,
.

**(b)** It is given that,

The
general equation for the electric field vector in the positive *x*
direction can be written as:

On comparing equations (1) and (2), we get

Electric
field amplitude, *E*_{0} = 3.1 N/C

Angular
frequency, *ω* = 5.4 × 10^{8} rad/s

Wave
number, *k* = 1.8 rad/m

Wavelength, = 3.490 m

**(c)** Frequency of wave is given as:

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

Where,

*c*
= Speed of light = 3 × 10^{8} m/s

**(e)** On observing the given vector field, it can be observed
that the magnetic field vector is directed along the negative z
direction. Hence, the general equation for the magnetic field vector
is written as:

**
**