Question

The magnetic field of an electromagnetic wave in a substance is given by $B=(2\times {10}^{-6}T)cos\left[\pi \right(0.04x+{10}^{7}t\left)\right]$ The refractive index of the substance is

• A. 1.2
• B. 2.5
• C. 1.33
• D. 1.5

Answer 1

The correct option is A 1.2

Comparing the given equation with standard EM wave equation,
$B=B_{0}cos(\omega t+kx)$,
We get, $\omega =\pi \times {10}^{7}rad/s$
$k=\pi \times \left(0.04\right)m^{-1}$
Speed of EM wave = $v=\frac{\omega }{k}=2.5\times {10}^{8}m/s$
Refractive index of substance =$\frac{c}{v}=\frac{3\times {10}^8}{2.5\times {10}^8}$
$=1.2$