JEE MAIN - Physics (2023 - 11th April Evening Shift - No. 2)
A plane electromagnetic wave of frequency $$20 ~\mathrm{MHz}$$ propagates in free space along $$\mathrm{x}$$-direction. At a particular space and time, $$\overrightarrow{\mathrm{E}}=6.6 \hat{j} \mathrm{~V} / \mathrm{m}$$. What is $$\overrightarrow{\mathrm{B}}$$ at this point?
$$-2.2 \times 10^{-8} \hat{i} T$$
$$2.2 \times 10^{-8} \hat{i} T$$
$$2.2 \times 10^{-8} \hat{k} T$$
$$-2.2 \times 10^{-8} \hat{k} T$$
Explanation
In free space, the relationship between the electric field (E) and the magnetic field (B) in an electromagnetic wave is given by:
$$ B = \frac{E}{c} $$
where c is the speed of light in a vacuum, approximately equal to $$3 \times 10^8 \mathrm{~m} / \mathrm{s}$$. We are given that the electric field is $$\overrightarrow{\mathrm{E}}=6.6 \hat{j} \mathrm{~V} / \mathrm{m}$$. To find the magnetic field, we can first calculate the magnitude of B:
$$ B = \frac{6.6 \mathrm{~V} / \mathrm{m}}{3 \times 10^8 \mathrm{~m} / \mathrm{s}} = 2.2 \times 10^{-8} \mathrm{~T} $$
Now, we need to find the direction of the magnetic field. Since the electromagnetic wave propagates in the x-direction, and the electric field is in the y-direction (j), the magnetic field should be in the z-direction (k) to satisfy the right-hand rule for electromagnetic waves. The direction of the magnetic field will be positive k (counter-clockwise rotation from x to y).
So, $$\overrightarrow{\mathrm{B}} = 2.2 \times 10^{-8} \hat{k} \mathrm{T}$$.
$$ B = \frac{E}{c} $$
where c is the speed of light in a vacuum, approximately equal to $$3 \times 10^8 \mathrm{~m} / \mathrm{s}$$. We are given that the electric field is $$\overrightarrow{\mathrm{E}}=6.6 \hat{j} \mathrm{~V} / \mathrm{m}$$. To find the magnetic field, we can first calculate the magnitude of B:
$$ B = \frac{6.6 \mathrm{~V} / \mathrm{m}}{3 \times 10^8 \mathrm{~m} / \mathrm{s}} = 2.2 \times 10^{-8} \mathrm{~T} $$
Now, we need to find the direction of the magnetic field. Since the electromagnetic wave propagates in the x-direction, and the electric field is in the y-direction (j), the magnetic field should be in the z-direction (k) to satisfy the right-hand rule for electromagnetic waves. The direction of the magnetic field will be positive k (counter-clockwise rotation from x to y).
So, $$\overrightarrow{\mathrm{B}} = 2.2 \times 10^{-8} \hat{k} \mathrm{T}$$.
Comments (0)
