Question

Assume a light bulb of power $P$ as a point source of electromagnetic radiation. The amplitude of electric field in the radiation at a distance $R$ from the source is ( C : speed of light)

• A. $\sqrt{\frac{P}{\pi {C\epsilon }_0{R}^2}}$
• B. $\sqrt{\frac{P}{2\pi {C\epsilon }_0{R}^2}}$
• C. $\sqrt{\frac{2P}{\pi {C\epsilon }_0{R}^2}}$
• D. $2\sqrt{\frac{P}{\pi {C\epsilon }_0{R}^2}}$

Answer 1

The correct option is C $\sqrt{\frac{2P}{\pi {C\epsilon }_0{R}^2}}$

Bulb of power $=P$

Point source of electromagnetic radiation. The amplitude of electric field in the radiation at a distance $=R$

$C=$ speed of light

$I_{ang}=\frac{{CB}_0^2}{{2\mu }_0}$ $({\mu }_0=P)$

or, $\frac{2P}{2\pi C{ϵ}_0{R}^2}=B_0^2$ or, $\frac{2P}{2\pi C{ϵ}_0{R}^2}=B_0^2$

$E=\frac{{qB}^{2}r}{m}$ (where $m=\frac{2}{\pi {ϵ}_0{R}^2}$)

Now, $E=\sqrt{\frac{2P}{\pi C{ϵ}_0{R}^2}}=E$