Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by \( E = 20 \, \sec(2 \times 10^{10}(t - 200x)) \, \text{V}/\text{m} \). The dielectric constant of the medium is equal to: (Take \( \mu_r = 1 \))
\( 2 \)
\( 9 \)
\( \tfrac{1}{3} \)
\( 3 \)
A plane electromagnetic wave with frequency of \( 30 \, \text{MHz} \) travels in free space. At particular point in space and time, electric field is \( 6 \, \text{V/m} \). The magnetic field at this point will be \( x \times 10^{-8} \, \text{T} \). The value of \( x \) is ________.
The electric field in an electromagnetic wave is given\( E = (50 \, \text{N C}^{-1}) \sin \omega (t - x / c) \)The energy contained in a cylinder of volume \( V \) is \( 5.5 \times 10^{-12} \, \text{J} \), The value of \( V \) is ________ \( \text{cm}^{3} \).(given \( \varepsilon_{0} = 8.8 \times 10^{-12} \, \text{C}^{2} \text{N}^{-1} \text{m}^{-2} \))
The magnetic field vector of an electromagnetic wave is given by \( \vec{B_0} = B_0 \dfrac{\hat{i} + \hat{j}}{\sqrt{2}} \cos(k z - \omega t) \); where \( \hat{i}, \hat{j} \) represents unit vector along \( x \) and \( y \)-axis respectively. At \( t = 0 \, \text{s} \), two electric charges \( q_1 \) of \( 4\pi \) coulomb and \( q_2 \) of \( 2\pi \) coulomb located at \( \left(0, 0, \dfrac{\pi}{k}\right) \) and \( \left(0, 0, \dfrac{3\pi}{k}\right) \), respectively, have the same velocity of \( 0.5\,c\,\hat{i} \), (where \( c \) is the velocity of light). The ratio of the force acting on charge \( q_1 \) to \( q_2 \) is:
The relative permittivity of distilled water is \( 81 \). The velocity of light in it will be: (Given \( \mu_r = 1 \))
An electromagnetic wave of frequency \( 3 \, \text{GHz} \) enters a dielectric medium of relative electric permittivity \( 2.25 \) from vacuum. The wavelength of this wave in that medium will be ________ \( \times 10^{-2} \, \text{cm} \).
A plane electromagnetic wave propagating along \( y -\)direction can have the following pair of electric field \( (\vec{E}) \) and magnetic field \( (\vec{B}) \) components.
A plane electromagnetic wave of frequency \( 100 \, \text{MHz} \) is travelling in vacuum along the \( x \)-direction. At a particular point in space and time, \( \vec{B} = 2.0 \times 10^{-8} \, \hat{k} \, \text{T} \). (where, \( \hat{k} \) is unit vector along \( z \)-direction) what is \( \vec{E} \) at this point? (speed of light \( c = 3 \times 10^{8} \, \text{m/s} \))
