Question

The electric field intensity produced by the radiations coming from 100 W bulb at a 3 m distance is E. The electric field intensity produced by the radiations coming from 50 W bulb at the same distance is:

• A. $\frac{E}{2}$
• B. 2E
• C. $\frac{E}{\sqrt{2}}$
• D. $\sqrt{2}$E

Answer 1

The correct option is A $\frac{E}{2}$

Power of bulb$=100W$

Intensity of Electric field at a distance 3m is E.

The electric field intensity is given by:

$E=\frac{P}{A}$

$\Rightarrow E=\frac{100}{\pi r^2}=\frac{100}{\pi \times 3^2}=\frac{100}{9\pi }watt/m^2$

Similarly, E at a distance of 3m produced by $50W$ bulb is:

$\Rightarrow E_1=\frac{50}{\pi r^2}watt/m^2=\frac{50}{9\pi }watt/m^2$

$\frac{E}{E_1}=\frac{100}{9\pi }÷\frac{50}{9\pi }$

$\Rightarrow \frac{E}{E_1}=\frac{100}{9\pi }\times \frac{9\pi }{50}=2$

$\Rightarrow E_1=\frac{E}{2}$