# If the magnetic field in a plane electromagnetic wave

Question:

If the magnetic field in a plane electromagnetic wave is given by $\vec{B}=3 \times 10^{-8} \sin \left(1.6 \times 10^{3} x+48 \times 10^{10} \mathrm{t}\right) \hat{j} \mathrm{~T}$, then what will be expression for electric field?

1. (1) $\vec{E}=\left(60 \sin \left(1.6 \times 10^{3} x+48 \times 10^{10} \mathrm{t}\right) \hat{k} \mathrm{v} / \mathrm{m}\right)$

2. (2) $\vec{E}=\left(9 \sin \left(1.6 \times 10^{3} x+48 \times 10^{10} \mathrm{t}\right) \hat{k} \mathrm{v} / \mathrm{m}\right)$

3. (3) $\vec{E}=\left(3 \times 10^{-8} \sin \left(1.6 \times 10^{3} x+48 \times 10^{10} \mathrm{t}\right) \hat{j} \mathrm{v} / \mathrm{m}\right)$

4. (4) $\vec{E}=\left(3 \times 10^{-8} \sin \left(1.6 \times 10^{3} x+48 \times 10^{10} \mathrm{t}\right) \hat{i} \mathrm{v} / \mathrm{m}\right)$

Correct Option: , 2

Solution:

(2) Given, $\vec{B}=3 \times 10^{-8} \sin \left(1.6 \times 10^{3} x+48 \times 10^{10} \mathrm{t}\right) \hat{j} T$

Using, $E_{0}=B_{0} \times C=3 \times 10^{-8} \times 3 \times 10^{8}=9 \mathrm{~V} / \mathrm{m}$

$\therefore \quad$ Electricfield, $\vec{E}=9 \sin \left(1.6 \times 10^{3} x+48 \times 10^{10} t\right) \hat{\mathrm{k}} V / m$