JEE Main 2023 — Electromagnetic Waves Question with Solution

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, $$\overrightarrow{\mathrm{B}}=2.2\times 10^{-8}\hat{k}\mathrm{T}$$.