Question 64: EM waves

Question

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?

Accepted Answer

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 $$3 	imes 10^8 \mathrm{~m} / \mathrm{s}$$. 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:
$$
B = \frac{6.6 \mathrm{~V} / \mathrm{m}}{3 	imes 10^8 \mathrm{~m} / \mathrm{s}} = 2.2 	imes 10^{-8} \mathrm{~T}
$$
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, $$\overrightarrow{\mathrm{B}} = 2.2 	imes 10^{-8} \hat{k} \mathrm{T}$$.

Answer

$$-2.2 	imes 10^{-8} \hat{i} T$$

Answer

$$2.2 	imes 10^{-8} \hat{i} T$$

Answer

$$2.2 	imes 10^{-8} \hat{k} T$$

Answer

$$-2.2 	imes 10^{-8} \hat{k} T$$

EM waves

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?

Choose the correct answer: