The electric field in a plane electromagnetic wave is given by Ez = 60cos(5x + 1.5×10^9t) V/m. Then the expression for the corres…

Question

The electric field in a plane electromagnetic wave is given by Ez = 60cos(5x + 1.5×10^9t) V/m. Then the expression for the corresponding magnetic field is (here subscripts denote the direction of the field):

1. A. By = 2×10^-7cos(5x + 1.5×10^9t) T (Correct answer)
2. B. Bx = 2×10^-7cos(5x + 1.5×10^9t) T
3. C. Bz = 60cos(5x + 1.5×10^9t) T
4. D. By = 60sin(5x + 1.5×10^9t) T

Correct Answer

Option A — By = 2×10^-7cos(5x + 1.5×10^9t) T

Detailed Solution & Explanation

The correct answer is Option A.

Key Points

• In an EM wave, $E$ and $B$ are in the same phase with $B_0=\dfrac{E_0}{c}$; $\vec E$, $\vec B$ and the propagation direction are mutually perpendicular.
• $B_0=\dfrac{60}{c}=\dfrac{60}{3\times10^{8}}=2\times10^{-7}$ T.
• $E$ is along $z$ and propagation is along $x$, so $B$ is along $y$: $B_y=2\times10^{-7}\cos(5x+1.5\times10^{9}t)$ T.