PYQ Bank

The electric field for a uniform plane wave in free space is given by \vec{E} = (\hat{x} + \hat{y})10 e^{j 10 z}. Determine the corresponding magnetic field vector.

The electromagnetic field inside a device is given by \vec{E} = \hat{y} E_0 \sin(k_x x) e^{-j k_z z}, \quad\text{where } k_x = \frac{n\pi}{a} \vec{H} = E_0 [\hat{x} \frac{-k_z}{\omega\mu} \sin(k_x x) + \hat{z} \frac{j k_x}{\omega\mu} \cos(k_x x)] e^{-j k_z z} Obtain an expression for the z-component of time-averaged Poynting vector \vec{S}.

Consider a perfectly conducting half-space as shown below :

A uniform plane wave given by

\begin{align*} \vec{E}^i &= \hat{x} E_0 e^{-j k z} \\ \vec{H}^i &= \hat{y} \frac{E_0}{\eta_0} e^{-j k z} \quad \eta_0 = 120\pi\text{ ohm} \end{align*}

is incident normally on the boundary. Write down the expressions for the reflected electric and magnetic fields.

For two isotropic media with \mu_1 \neq \mu_2 and \varepsilon_1 \neq \varepsilon_2, find an expression for the Brewster angle \theta_b for parallel polarization.

A wire of length 2 m is perpendicular to X-Y plane. It is moved with a velocity \vec{V}=(2\hat{i}+3\hat{j}+\hat{k})\,\mathrm{ms}^{-1} through a region of uniform induction \vec{B}=(\hat{i}+2\hat{j})\mathrm{Wm}^{-2}. Compute the potential difference between the ends of the wire.

Consider the L\text{-}C\text{-}R circuit shown below :

\begin{align*} R &= 0\cdot 1\ \Omega \\ L &= 1\text{ nH} \\ C &= 1\text{ nF} \end{align*}

(i) Determine its resonance frequency f_0.

Consider a long, line charge with charge density \rho_l = 10^{-6}\text{ coulomb/m}. Find the force acting on a dust particle carrying -10^{-9}\text{ coulomb}, 1\text{ metre} away from the line charge in free space.

A spherical capacitor is made of concentric conductors of radii a and b (b > a). The total charge on the inner sphere of radius a is Q. (i) Derive an expression for the capacitance C.

(ii) The earth may be modeled as a spherical capacitor with a = 6\cdot 5 \times 10^6\text{ m} and b \rightarrow \infty. Determine C, if the medium surrounding the earth is free space.

A point charge +q is located near the corner of a horizontal and a vertical plate as shown below :

Obtain an expression for the electrostatic potential \phi_P using the image method.

A long wire of radius a carries I amperes of current. The magnetic field surrounding it is given by H_\phi = \dfrac{I}{2\pi\rho} for \rho > a. Obtain expressions for (i) the magnetic energy stored per unit length in the region b \ge \rho \ge a and (ii) the equivalent inductance L per unit length.

If the magnetic moment of proton is 2.793\ \mu_N calculate, giving necessary steps, the radio frequency at which nuclear magnetic resonance occurs in water kept in a uniform magnetic field of 2.4\text{ T}.

Using Maxwell's field equations for a homogeneous non-conducting medium, derive the wave equation for the electric field. Calculate the velocity of EM wave in free space.

Explain the term 'Poynting vector' and state the significance of Poynting theorem.

Calculate the skin depth for radio waves in free space of wavelength 3 m in copper, given that electrical conductivity for copper is 6\times10^{7}\,\Omega^{-1}\,\mathrm{m}^{-1}.

The following inputs are given :

\begin{align*} T_0 &= 5500\text{ K} && \text{(Sun surface temperature)}, \\ R &= 7 \times 10^{10}\text{ cm} && \text{(Sun radius)}, \\ r &= 6\cdot 4 \times 10^8\text{ cm} && \text{(Earth radius)}, \\ D &= 1\cdot 5 \times 10^{13}\text{ cm} && \text{(Sun--Earth distance)}. \end{align*}

Assume that the earth and the sun both absorb all electromagnetic radiations incident on them, and that the earth is at a constant temperature T over the day-night cycle. Calculate T.

Show that when the temperature T of a radiating object is not too different from the surrounding temperature T_0, the object obeys Newton's law of cooling.

A radiation gas of temperature T fills a cavity of volume V. The system expands adiabatically and reversibly to a volume equal to 8V. By what factor does the temperature change?

What happens if the primary winding of a transformer is connected to a battery?

Discuss the growth of current when an e.m.f. is suddenly applied to a circuit containing resistance, inductance and capacitance in series. What is the time constant of the circuit?