Electromagnetic Waves - Electricity - Physics Previous Year Questions

In terms of potential difference V, electric current I, permittivity \({\varepsilon _0}\), permeability \({\mu _0}\) and speed of light c, the dimensionally correct equation(s) is(are) :

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, \([E]\) and \([B]\) stand for dimensions of electric and magnetic fields respectively, while \(\left[ {{\varepsilon _0}} \right]\) and \(\left[ {{\mu _0}} \right]\) stand for dimensions of the permittivity and permeability of free space respectively. \(\left[ L \right]\) and \(\left[ T \right]\) are dimensions of length and time respectively. All the quantities are given in \(SI\) units.

The relation between \(\left[ {{\varepsilon _0}} \right]\) and \(\left[ {{\mu _0}} \right]\) is

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, \([E]\) and \([B]\) stand for dimensions of electric and magnetic fields respectively, while \(\left[ {{\varepsilon _0}} \right]\) and \(\left[ {{\mu _0}} \right]\) stand for dimensions of the permittivity and permeability of free space respectively. \(\left[ L \right]\) and \(\left[ T \right]\) are dimensions of length and time respectively. All the quantities are given in \(SI\) units.

The relation between \([E]\) and \([B]\) is

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $\vec{E}=30(2 \hat{x}+\hat{y}) \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^7}{3} z\right)\right] \mathrm{Vm}^{-1}$. Which of the following option(s) is(are) correct?

[Given: The speed of light in vacuum, $c=3 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$ ]

A cube of unit volume contains $35 \times 10^7$ photons of frequency $10^{15} \mathrm{~Hz}$. If the energy of all the photons is viewed as the average energy being contained in the electromagnetic waves within the same volume, then the amplitude of the magnetic field is $\alpha \times 10^{-9} \mathrm{~T}$. Taking permeability of free space $\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}$, Planck's constant $h=6 \times 10^{-34} \mathrm{Js}$ and $\pi=\frac{22}{7}$, the value of $\alpha$ is ____________.

The electric field associated with an electromagnetic wave travelling in vacuum is given by

$E_0 \sin(3y + 4z + \omega t) \hat{i}$, where $\\omega$ is the angular frequency. All quantities are in SI units. The correct statement(s) about this wave is/are:

[Given: speed of light in vacuum $c = 3 \times 10^8\ \mathrm{m\,s^{-1}}$.]