Question

An electromagnetic wave is radiated by a $100$ W bulb. If efficiency of the bulb is $20$ then the amplitude of magnetic field at a distance of $1$ m is (Consider bulb as a point source)

Answer 1

Given power of bulb $P=100W$ and efficiency $\eta =20$%

Now the surface area of the surrounding sphere considering bulb as a point source which radiates electromagnetic

wave $A=4\pi r^2$ where r= distance between the bulb and magnetic filed $=1m$

$A=12.56m^2$

Now intensity at a distance of 1 m$I=\frac{Power}{Area}=\frac{100\times 0.20}{12.56}=1.59$

Also we know

$\frac{1}{2}I=\frac{1}{2}\left({ϵ}_0{E}_{rms}^{2}C\right)$

$E_{rms}=\sqrt{\frac{I}{{ϵ}_{0}C}}$ where C= speed of light in air$=3\times {10}^8$ and ${ϵ}_0$=permeability$=8.85\times {10}^{-12}$

$E_{rms}=\sqrt{\frac{1.59\times {10}^4}{8.85\times 3}}=24.48$

Again we know Amplitude $A^2=E$

$A=\sqrt{24.48}=4.98$