Question

A sinusoidal electromagnetic wave is propagating in a vacuum in the +z-direction.

Part A

If at a particular instant and at a certain point in space the electric field is in the +x-direction and has a magnitude of 3.40V/m , what is the magnitude of the magnetic field of the wave at this same point in space and instant in time?

Part B

What is the direction of the magnetic field?

Answer 1

Concepts and reason

The concepts required to solve the given questions is electric and magnetic field in an electromagnetic wave.

Initially, write an expression for the relation between the electric field and the magnetic field in an electromagnetic wave. Later, calculate the magnetic field. Finally, calculate the direction of the magnetic field.

Fundamentals

The expression for the relation between the electric field and the magnetic field in an electromagnetic wave is as follows:

$c = \frac{{{E_0}}}{{{B_0}}}$

Here, c is the speed of light, ${E_0}$ is the amplitude of the electric field, and ${B_0}$ is the amplitude of the magnetic field.

(A)

Rearrange the equation $c = \frac{{{E_0}}}{{{B_0}}}$ for ${B_0}$ as follows:

${B_0} = \frac{{{E_0}}}{c}$

Substitute $3 \times {10^8}{\rm{ m/s}}$ for c and 3.40 V/m for ${E_0}$ in the equation ${B_0} = \frac{{{E_0}}}{c}$ .

$\begin{array}{c}\\{B_0} = \frac{{3.40{\rm{ V/m}}}}{{3 \times {{10}^8}{\rm{ m/s}}}}\\\\ = 1.13 \times {10^{ - 8}}{\rm{ T}}\\\end{array}$

(B)

The direction of electric field is pointing in the positive x direction and the direction of propagation of wave is in the positive z direction. Therefore, the direction of the magnetic field is in the positive y direction. Because in an electromagnetic wave, the direction of electric field, the direction of wave propagation, and the magnetic field all lie perpendicular to each other.

Ans: Part A

The magnitude of the magnetic field is equal to $1.13 \times {10^{ - 8}}{\rm{ T}}$ .

Part B

The direction of magnetic field is in the positive y direction.