Question

At what distance from a $10W$ point source of electromagnetic waves is the magnetic field amplitude $1.0mT$?

Short answer

Distance,$d=0.0816\mathrm{m}$

Step-by-step solution

Electromagnetic waves

EM waves are waves that are formed when an electrical field and a physical phenomenon vibrate together.

Find Average Current

Given Values:

$P=10\mathrm{W}$

$B_o=1\times {10}^{-6}\mathrm{T}$

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

we know that:

$E_o=\left(3\times {10}^8\right){10}^{-6}$

$E_o=300:\mathrm{V}/\mathrm{m}$

Now,

$E_o^2=\frac{2I_{avg}}{c·{\epsilon }_o}$

$I_{avg}=\frac{c·{\epsilon }_o{E}^2}{2}$

$I_{avg}=\frac{3\times {10}^8\times 8.85\times {10}^{-12}\times (300{)}^2}{2}$

$l_{avg}=119.47$

Find Distance

Average Current,

$I_{avg}=\frac{P}{\text{spherical area}}$

$119.47=\frac{10}{4\pi d^2}$

$4\pi d^2=\frac{10}{119.47}$

$d={\left(\frac{0.0837}{4\times \pi }\right)}^{1/2}$

$d=0.0816\mathrm{m}$