[2018EM/MidSem]

Electrodynamics                                                             Sep 26 ,2018

Mid Semester Examination

• A conducting spherical shell of radius \(a\) is placed in a uniform field \(\vec{E}\). Show that the force tending to separate two halves of the sphere across a diametrical plane perpendicular to \(\vec{E}\) is given by \[F = \frac{9}{4}\pi \epsilon_0a^2 E^2.\]
• Compute the potential due to a uniformly polarized infinitely long cylinder of radius \(a\) at points (i) inside and (ii) outside the cylinder. Show that the is same as that of a conductor raised to some potential \(V_0\). Find relation between \(V_0\) and the polarization.
• A long conducting coaxial cable consists of a copper wire of radius \(a\), surrounded by concentric copper tube of inner radius \(c\). The space in between is partially filled from (\(b\) to \(c\) ) with material of dielectric constant \(\kappa\) as shown in figure below. Find the capacitance per unit length of this cable.
• Suppose entire region below the plane \(z=0\) is filled with uniform linear dielectric material of susceptibility \(\xi_1\) and the region above the plane is filled with a linear dielectric of susceptibility \(\chi_2\). A point charge \(Q\) is placed at \(z=d\) above the origin. Find the potential everywhere. What is the force acting on the point charge?