In a plane electromagnetic wave, the electric field varies as $E_z = 90\sin(500x + 20 × 10^{10}t) V/m$. The expression of its magnetic field variation is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $3 × 10^{-7} \sin(500x + 20 × 10^{10}t) T$
Given electric field:
$E_z = 90 \sin(500x + 2.0 \times 10^{11}t)$ V/m
Relation between $E$ and $B$ in an electromagnetic wave:
$\frac{E}{B} = c$
$\Rightarrow B = \frac{E}{c}$
Maximum electric field:
$E_0 = 90$ V/m
So, maximum magnetic field:
$B_0 = \frac{90}{3 \times 10^8} = 3 \times 10^{-7}$ T
Since $E$ is along z-axis and wave is propagating along negative x-axis (from argument $500x + \omega t$), the magnetic field will be along y-axis.
Thus, the magnetic field expression is:
$B_y = 3 \times 10^{-7} \sin(500x + 2.0 \times 10^{11}t)$ T