JEE MAIN - Physics (2024 - 6th April Evening Shift - No. 20)
Explanation
To find the intensity of the given electromagnetic wave, we need to use the formula for the intensity of an electromagnetic wave:
$$ I = \frac{1}{2} \epsilon_0 c E_0^2 $$
where:
- $$I$$ is the intensity in $$\mathrm{W} / \mathrm{m}^2$$
- $$\epsilon_0$$ is the permittivity of free space, given as $$9 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$$
- $$c$$ is the speed of light in vacuum, approximately $$3 \times 10^8 \mathrm{~m/s}$$
- $$E_0$$ is the peak electric field, given as $$600 \mathrm{Vm}^{-1}$$
Now, substitute these values into the formula:
$$ I = \frac{1}{2} \times 9 \times 10^{-12} \times 3 \times 10^8 \times (600)^2 $$
Simplify the expression step-by-step:
$$ I = \frac{1}{2} \times 9 \times 10^{-12} \times 3 \times 10^8 \times 360000 $$
First, calculate $$9 \times 3 \times 360000$$:
$$ I = \frac{1}{2} \times 9.72 \times 10^{-4} \times 360000 $$
Combine 9 and 3 into 27, giving you:
$$ I = 13.5 \times 10^{-4} \times 360000 $$
Then, calculate the multiplication:
$$ I = 13.5 \times 36 $$
Finally, multiply the remaining values:
$$ I = 486 \times 10^{-4} $$
The final value is:
The intensity, $$I$$, is 486 $$\mathrm{W} / \mathrm{m}^2$$. Therefore, the correct option is:
Option A: 486
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