Question

The magnetic field in a traveling electromagnetic wave has a peak value of $20\mathrm{nT}.$ What is the peak value of electric field strength?

Answer 1

The peak value of electric field strength:

1. The peak value of electric field strength is known as the product of the peak value of the magnetic field and velocity of light.
2. By substituting the value of magnetic field and velocity of light we get the value of peak electric field strength.
3. Hence in the case, of the Electromagnetic wave, the magnitude of the electric field is said to be proportional to the magnitude of the magnetic field.

Step 1: Given data:

The peak value of the magnetic field in a traveling electromagnetic wave is given by= $20\mathrm{nT}=20\times {10}^{-9}\mathrm{T}$

The peak value of the electric field=?
Step 2: Formula for the calculation of peak value of the electric field :

We already know that the peak value of electric field strength can be given as the product of the peak value of the magnetic field and the velocity of light.
${\mathrm{E}}_0=\mathrm{c}{\mathrm{B}}_0$
Where,
${\mathrm{E}}_0$ is the electric field
$B_0$ is the magnetic field
$\mathrm{C}$ is the velocity of light$=3\times {10}^8\mathrm{m}/\mathrm{s}$
Step 3: Calculation of peak value of the electric field :
Substituting the given values in the above equation, we can calculate the peak value of the electric field as:
$$\begin{gathered} {\mathrm{E}}_0=3\times {10}^8\times 20\times {10}^{-9} \\ =6\mathrm{V}/\mathrm{m} \end{gathered}$$
Hence, the peak value of electric field strength is $6\mathrm{v}/\mathrm{m}$.