Question

A plane electromagnetic wave in a non magnetic dielectric medium is given by $\overline{E}=\overline{E_0}(4\times {10}^{-7}\times -50t)$ with distance being in meter and time in seconds. The dielectric constant of the medium is:

• A. 2.4
• B. 5.8
• C. 8.2
• D. 4.8

Answer 1

Answer: (B)

Given equation of wave

$\overrightarrow{E}={\overrightarrow{E}}_0(4\times \overrightarrow{10}x-50t)$

Comparing with general equation of wave,

$\overrightarrow{E}={\overrightarrow{E}}_0(kx-wt),$

we get,

$w=50rad/s.$ $k=4\times {10}^{-7}{m}^{-1}$

Thus velocity of wave,

$v=\frac{w}{k}=\frac{50}{4\times {10}^{-7}}=1.25\times {10}^{8}m/s$

so, refractive index of medium,

$\mu =\frac{e}{v}=\frac{3\times {10}^8}{1.25\times {10}^8}=2.4$

using,

$u^2=km.ke$ [km and ke are magnetic and dielectric di - constants]

as medium is non diamagnetic, $km=1$

$\Rightarrow ke={\mu }^2=(2.4{)}^2\Rightarrow ke=5.76$