Question

What is the maximum electric field strength in an electromagnetic wave that has a maximum magnetic field strength of \(5.00 \times {10^{ - 4}}\;T\) (about \(10\) times the Earth's)?

Short answer

The maximum electric field strength value is obtained as \(15 \times {10^4}\;V/m\).

Step-by-step solution

Definition of electromagnetic wave

Examples of waves transmitted by concurrent periodic changes in the strength of the electric and magnetic fields include radio waves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

Given Information

• The magnetic field strength: \(5.00 \times {10^{ - 4}}\;T\)

Find the maximum electric field strength in an electromagnetic wave

The formula for calculating the strength of an electric and magnetic field is:

\(E = Bc\)

Here\(E = \)Electric field,\(C = \)speed of light,\(B = \)Magnetic field

Now we must enter the value of\(B\)as it appears in the question,\(c = 3.00 \times {10^8}\;m{s^{ - 1}}\)

\(\begin{aligned} E{\rm{ }} &= Bc\\ &= \left( {5.00 \times {{10}^{ - 4}}T} \right)\left( {3.00 \times {{10}^8}\;m{s^{ - 1}}} \right)\\ &= 15 \times {10^4}\left( {\;V.s/{m^2}} \right)\left( {m{s^{ - 1}}} \right)\\ &= 15 \times {10^4}\;V/m\end{aligned}\)

As a result, the electric field strength is\(E = 15 \times {10^4}\;V/m\).