# A sinusoidal electromagnetic wave is propagating in vacuum in the +z-direction. If at a particular instant and at a certain point in space t

Question

A sinusoidal electromagnetic wave is propagating in vacuum in the +z-direction. If at a particular instant and at a certain point in space the electric field is in the +x-direction and has magnitude 3.20 V/m, what are the magnitude and direction of the magnetic field of the wave at this same point in space and instant in time?

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2 years 2021-07-26T14:28:46+00:00 1 Answers 40 views 0

The magnitude of the magnetic field is $$B_o = 1.13 *10^{-8}T$$

The direction is in the +y direction

Explanation:

From the question we are told that

The electric field is $$E_o = 3.40 \ V/m$$

The relationship between electric and magnetic field is mathematically represented  as

$$c = \frac{E_o}{B_o}$$

Where  c is the speed of light

$$B_o$$ is the magnetic field

Making $$B_o$$  the subject off the formula

$$B_o = \frac{E_o}{c}$$

$$= \frac{3.40}{3*10^{8}}$$

$$B_o = 1.13 *10^{-8}T$$

Generally in an electromagnetic wave the direction of the wave propagation , the electric field and the magnetic field are perpendicular

Since from the question the direction of the electric field is +x direction and the  wave  propagation is in the + z direction then the magnetic field would be in the + y direction