Question

A plane electromagnetic wave traveling in the positive  direction of an x axis in vacuum has components E_x = E_y = 0  and

E_z = (4.8 V/m) cos[(?

Answer 1

according to given problem , we have

x, y , z - components of the electeomagnetic waves is

E_x = E_y = 0 and E_z = (4.8 V/m) cos[(?*10¹⁵ s^-1)(t - x/c)]

here , maximum electric field E_m = 5 V/m

a)

the amplitude of the magnetic field is

B_m = E_m/c

= (4.8 V/m) / ( 2.998*10⁸ m/s)

= 1.601*10^-8 T

b)

from given problem ,

the waves oscillates in z-direction and its travels in +ve x-direction.

so , B_x = B_z = 0

therefore , the oscillation of the magnetic field is parallel to the y-axis.

c)

electromagnetic wave propagation is determined by E*B.

( * = cross product)

if the electric field component is in the positive direction of the z axis ,

then the magnetic field is in the y-axis (direction)

B_y = B_m cos[(?*10¹⁵ s^-1)(t - x/c)]

= (1.601*10^-8 T) cos[(?*10¹⁵ s^-1)(t - x/c)]

Answer 2

according to given problem , we have

x, y , z - components of the electeomagnetic waves is

E_x = E_y = 0 and E_z = (4.8 V/m) cos[(?*10¹⁵ s^-1)(t - x/c)]

here , maximum electric field E_m = 5 V/m

a)

the amplitude of the magnetic field is

B_m = E_m/c

= (4.8 V/m) / ( 2.998*10⁸ m/s)

= 1.601*10^-8 T

b)

from given problem ,

the waves oscillates in z-direction and its travels in +ve x-direction.

so , B_x = B_z = 0

therefore , the oscillation of the magnetic field is parallel to the y-axis.

c)

electromagnetic wave propagation is determined by E*B.

( * = cross product)

if the electric field component is in the positive direction of the z axis ,

then the magnetic field is in the y-axis (direction)

B_y = B_m cos[(?*10¹⁵ s^-1)(t - x/c)]

= (1.601*10^-8 T) cos[(?*10¹⁵ s^-1)(t - x/c)]