JEE MAIN - Physics (2023 - 30th January Evening Shift - No. 10)
A point source of $100 \mathrm{~W}$ emits light with $5 \%$ efficiency. At a distance of $5 \mathrm{~m}$ from the source, the intensity produced by the electric field component is:
$\frac{1}{40 \pi} \frac{W}{m^2}$
$\frac{1}{10 \pi} \frac{W}{m^2}$
$\frac{1}{20 \pi} \frac{W}{m^2}$
$\frac{1}{2 \pi} \frac{W}{m^2}$
Explanation
A point source of $100 \mathrm{~W}$ emits light with $5 \%$ efficiency. At a distance of $5 \mathrm{~m}$ from the source, the intensity produced by the electric field component is evaluated as follows:
The intensity at a distance of $5$ meters can be calculated as:
Intensity at 5 m $$= \frac{5}{4\pi \times 5^2}\left(\frac{W}{m^2}\right)$$
$$= \frac{1}{20\pi}\left(\frac{W}{m^2}\right)$$
Since the intensity due to the electric field component is half of the total intensity:
Intensity due to electric field $$= \frac{1}{40\pi}\left(\frac{W}{m^2}\right)$$
Thus, we arrive at our result:
$$= \frac{1}{40\pi}\left(\frac{W}{m^2}\right)$$
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