A vertically oriented electric dipole having dipole moment \vec{p} is kept at height h above an infinitely large horizontal conducting plate, which is grounded as shown in the diagram. Calculate the force between the electric dipole and the conducting plate by using method of images.
Using the two-fluid model of a conductor (normal and superconducting) and the Maxwell's equations, derive the two London equations of superconductivity.
For the electric field given by E=E_0e^{i\omega t}, show that the conduction current is in phase with the electric field, while the displacement current leads the electric field by \frac{\pi}{2} radians. Also, show that the displacement current in a good conductor is negligible compared to the conduction current at any frequency lower than the optical frequencies (f<10^{15}\ \mathrm{Hz}).
Write Maxwell's equations in free space in both differential and integral forms. Obtain wave equations and show that electromagnetic waves can travel in free space with a speed of light. Can one get the wave equations from the integral form of the Maxwell's equations?
Find the values of \mathrm{E} and \mathrm{H} on the surface of a wire carrying a current. By computing the Poynting vector, show that it represents a flow of energy into the wire.
Briefly outline the theory of scattering of electromagnetic radiation by a bound electron and hence derive the conditions for Rayleigh scattering. How can you explain the blue of the sky?
Discuss in brief the ultraviolet catastrophe. How did Planck solve this problem?
Three cells are connected in parallel with similar poles connected together with wires having negligible resistance. The emfs of the cells are 2, 1 and 4 volts respectively and the corresponding internal resistances are 4, 3 and 2 ohms. Calculate the current flowing through the 4 V cell.
Why do we prefer to work with a critically damped ballistic galvanometer in a laboratory? What is external critical damping resistance?
Two conducting planes, intersecting at right-angles to each other, are kept at a potential \phi_0. Calculate the potential at a point in space if the total charge on a plane of area \alpha be Q.
Find the capacitance of two concentric spherical metal shells having radii a and b.
Starting from the expression for the electrostatic potential \phi(\vec{r})=\frac{1}{4\pi\varepsilon_0}\int_V\frac{\rho(\vec{r}_0)}{|\vec{r}-\vec{r}_0|}\,dV_0 obtain Poisson's equation \nabla^2\phi=-\frac{\rho}{\varepsilon_0}. [Symbols have their usual meanings]
Write down Maxwell's equations in integral form. Explain the significance of each of these equations.
A uniformly magnetized sphere of radius R has magnetization \vec{M}=M_0\hat{z}. If the scalar magnetic potentials inside and outside the sphere are given as under \phi_m=\frac{M_0}{3}z;\ r\leq R and \phi_m=\frac{M_0R^3}{3r^2}\cos\theta;\ r>R where, r,\theta are two spherical coordinates, find the magnetic field inside and outside the sphere.
A 0.5\,\mathrm{m} long cylindrical medium between two conducting plates has uniform charge density of 100\,\mathrm{nC/m^3}. The axis of the cylindrical medium is along z-axis. The left plate is at z=0 and has a potential of 10\,\mathrm{kV} and the right plate is grounded. Determine the electric field at axial distance z=0.2\,\mathrm{m}.
Two solenoids have 500 and 800 turns of wire and are placed co-axially close to each other. A current of 5.0 A in the first solenoid produces an average flux of 200\mu\mathrm{Wb} through its each turn and a flux of 100\mu\mathrm{Wb} through each turn of the second solenoid. Find the self-inductance of the first solenoid and the mutual inductance of the solenoids.
A parallel plate capacitor has plate area =4.0\ \mathrm{cm^2} and plate separation =2.0\ \mathrm{mm}. An a.c. voltage V=20\sin(5\times10^{3}t) volts is applied across the plates. If the dielectric constant of the medium between the plates is \varepsilon_r=2.0, calculate the displacement current.
A 12.0 V battery is connected at t=0 to a series combination of a resistor R=10.0\Omega and an inductor L=5.0\mathrm{H}. At what rate is energy being stored in the inductor when the current in the circuit is 0.4 A?
A current carrying circular wire loop of radius 1.0 cm has a magnetic moment 2.0\,\mathrm{mJ/T}. Determine the magnetic field at an axial distance of 3.0 cm from the centre of the loop.
What are the limitations of Rayleigh-Jeans law in explaining the spectrum of radiations from a blackbody? Explain how these limitations were overcome in Planck's radiation law. Deduce Wien's displacement law from Planck's radiation law.