Question

A plane electromagnetic wave propagating in the $x-$direction in vacuum has wavelength of $6.0\text{mm}$. The electric field is in the $y-$direction and its maximum magnitude is $33{\text{Vm}}^{-1}$.

$\left(i\right)$ The equation for the electric field as a function of $x\left(\text{m}\right)$ and $t\left(\text{s}\right)$ is.

​​​​​​​$[$1 Mark$]$

• A. $11\sin \left[\pi (t-\frac{x}{c})\right]$
• B. $33\sin [\pi \times {10}^{11}(t-\frac{x}{c})]$
• C. $33\sin \left[\pi (t-\frac{x}{c})\right]$
• D. $11\sin [\pi \times {10}^{-11}(t-\frac{x}{c})]$

Answer 1

The correct option is B $33\sin [\pi \times {10}^{11}(t-\frac{x}{c})]$

The equation for the electric field along y-axis in the electromagnetic wave is given by
$E_y=E_0\sin \omega [t-\frac{x}{c}]$

Here $\omega =2\pi f=\frac{2\pi c}{\lambda }=\frac{2\pi \times 3\times {10}^8}{6\times {10}^{-3}}=\pi \times {10}^{11}\text{rad}{\text{s}}^{-1}$

$E_0=33{\text{Vm}}^{-1}$ (given)

$E_y=33\sin [\pi \times {10}^{11}(t-\frac{x}{c})]$