Question

For a certain sinusoidal wave of intensity I, the amplitude of the magnetic field is B. What would be the amplitude (in terms of B) in a similar wave of twice the intensity?

Short answer

The amplitude of a wave of twice the intensitywill increase by a factor of$\sqrt{2}$.

Step-by-step solution

Formula for intensity of electromagnetic wave. 

The intensity of a wave is calculated by $I=\frac{c}{2\cdot {\mu }_0}\cdot B^{2}max$where c is the speed of light and${\mu }_0=4\cdot \pi \cdot {10}^{-7}\frac{H}{\mathrm{m}}$which is the permeability of space.

Determining the amplitude of B’ .

Let $I\text{'}=2I$

Substitute the values using the formula of intensity and equating for B.

$$\begin{gathered} \frac{c}{2.{\mu }_0}.B{\text{'}}^2=2*\frac{c}{2.{\mu }_0}.B^2 \\ {B}^{\text{'}2}=2*B^2 \\ {B}^{\text{'}}=\sqrt{2}*B^2 \end{gathered}$$

Therefore the amplitude of B’ will be increase $\sqrt{2}$times then that of B.