Question

a. What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is $100\mathrm{V}/\mathrm{m}$$?$

b. What is the intensity of the wave$?$

Short answer

a.Magnetic field amplitude of an electromagnetic wave is $3.33\times {10}^{-7}\mathrm{T}$.

b.Intensity of the wave is$13.2813\mathrm{W}/{\mathrm{m}}^2$.

Step-by-step solution

Formula for magnetic field amplitude and intensity

The amplitude of a magnetic field is,

$\left|{\mathrm{B}}_{\mathrm{o}}\right|=\frac{\left|\mathrm{E}\right|}{\mathrm{c}}$

Intensity,

$\mathrm{I}=\frac{1}{2}{\mathrm{E}}_{\mathrm{o}}{\left|{\mathrm{E}}_{\mathrm{o}}\right|}^2\mathrm{c}$

localid="1648794396885" $\mathrm{c}$-Speed of the light in vacuum

Calculation for magnetic field amplitude of an electromagnetic wave (part a)

(a).

As it stands,

$\left|{\mathrm{E}}_{\mathrm{o}}\right|=100\mathrm{V}/\mathrm{m}$

$\mathrm{c}=3\times {10}^8\mathrm{m}/\mathrm{s}$

$\left|{\mathrm{B}}_{\mathrm{o}}\right|=\frac{\left|\mathrm{E}\right|}{\mathrm{c}}$

$\left|{\mathrm{B}}_{\mathrm{o}}\right|=\frac{100\mathrm{V}/\mathrm{m}}{3\times {10}^8\mathrm{m}/\mathrm{s}}$

$\left|{\mathrm{B}}_{\mathrm{o}}\right|=3.33\times {10}^{-7}\mathrm{T}$

Calculation for intensity of wave (part b)

(b).

As it stands,

$\left|{\mathrm{E}}_{\mathrm{o}}\right|=100\mathrm{V}/\mathrm{m}$

$\mathrm{c}=3\times {10}^8\mathrm{m}/\mathrm{s}$

$\mathrm{I}=\frac{1}{2}{\mathrm{E}}_{\mathrm{o}}{\left|{\mathrm{E}}_{\mathrm{o}}\right|}^2\mathrm{c}$

$\mathrm{I}=\frac{1}{2}100|100{|}^2\times 3\times {10}^8$

$\mathrm{I}=13.2813\mathrm{W}/{\mathrm{m}}^2$