Discuss briefly the features of 'guard rings'. The plates of a capacitor are square-shaped, each of side l. The plates are inclined at an angle \alpha to each other. The smallest distance between the plates is a. Calculate the capacitance when \alpha is small.
Why does a soap bubble expand upon electrification? A sphere of radius R contains a charge +Q and a charge -Q distributed uniformly in the upper and lower hemispheres respectively. Show that the dipole moment of charge distribution is \dfrac{3}{4}QR\hat{k}, where \hat{k} is directed along the polar axis of the spherical coordinate system.
How does one explain the observed spectrum of black-body radiation using Planck's quantum hypothesis ? State and obtain Wien's displacement law. Also explain the important features of this law.
A current i(t)=(2e^{-t}-e^{-2t})\,\mu\mathrm{A} charges up a 120\,\mathrm{nF} capacitor for a period of 2 seconds. If the final voltage across the capacitor is 15\,\mathrm{V}, what was the initial voltage across it?
How large an inductance needs to be connected in series with a 120 V, 60 W lightbulb if it is to operate normally when the combination is connected across a 240 V, 60 Hz supply?
Discuss the principle of 'artificial dielectric'. Where do you find its use?
When a person carrying something metallic walks through the doorway of a metal detector, it emits a sound. Explain the reason behind it. A 200\Omega resistor and a 15\mu\mathrm{F} capacitor are connected in series to 220 V, 50 Hz a.c. supply. Calculate the current in the circuit and the r.m.s. voltage across the resistor and the capacitor. Is the algebraic sum of these voltages more than the supply voltage? If yes, resolve the paradox.
A charge q=2\,\mu\mathrm{C} is placed at a=10\,\mathrm{cm} from an infinite grounded conducting plane sheet. Find the (i) total charge induced on the sheet, (ii) force on the charge q and (iii) total work required to remove the charge slowly to an infinite distance from the plane.
(i) State Faraday's law of electromagnetic induction and prove that it can be expressed in the following vector form : \mathrm{Curl}~\vec{E} = -\frac{\partial \vec{B}}{\partial t} with \vec{E} and \vec{B} being the electric and magnetic fields. (ii) A coil of 10 turns has dimension 9~\text{cm} \times 7~\text{cm}. It rotates at the rate of 15\pi~\text{rad/sec} in a uniform field whose flux density is 0\cdot 6~\text{weber/m}^2. What is the maximum e.m.f. induced in the coil ?
(i) Using Maxwell's equations, obtain the relation \frac{1}{c} \frac{\partial}{\partial t} \left( \frac{E^2 + B^2}{2} \right) + \vec{\nabla} \cdot (\vec{E} \times \vec{B}) = 0 (ii) What is Poynting vector ? Deduce Poynting theorem for the flow of energy in an electromagnetic field.
Discuss the reflection and refraction of plane electromagnetic waves at plane dielectric boundaries for normal incidence and also find the reflection and transmission coefficients.
Write down the four Maxwell's equations and explain the contribution of Maxwell in the development of these equations.
Use the method of electric images to find the electric field on the surface of a grounded conducting sphere.
(i) Define and explain the significance of the quality factor of an electrical machine. (ii) Discuss in brief, the working principle of a transformer.
Show that Maxwell's equations of electrodynamics are invariant under Lorentz transformations.
Show that for any electromagnetic wave propagating in free space, the total average energy per unit volume is \frac{1}{2}\epsilon_0 E_{\text{max}}^2; where E_{\text{max}} is the amplitude of the electric field associated with the electromagnetic wave.
(i) Derive Planck's law of Black body radiation. (ii) Obtain its limiting forms for (i) very low frequency and (ii) very high frequency.
What is the volume density of charge in a region of space where electrostatic potential is given by V = a - b(x^2 + y^2) - c\log(x^2 + y^2), where a, b, c are constants.
A point charge of q is held above a grounded conducting plane located at z = 0. If the position of the charge is (0, 0, d), obtain an expression for the induced charge density on the plane as a function of the coordinates x and y.
If the magnetic field \vec{B}, at a point with position vector \vec{r} is uniform, show that the corresponding vector potential \vec{A}(\vec{r}) is given by \vec{A}(\vec{r}) = -\frac{1}{2} \left[ \vec{r} \times \vec{B} \right]
