[2018EM/HMW-02]

Electrodynamics                                                                           Aug 13, 2018

Tutorial II

1. Show that the potential due to a spherical shell with uniform surface charged density \(\sigma\) everywhere inside the shell is \(\frac{Q}{4\pi\epsilon_0 R}\), where \(Q\) is the total charge on the shell.
2. Compute the electrostatic energy of a uniformly charged solid sphere with total charge \(Q\).
3. Obtain an expression for electrostatic energy of a thin charged conducting shell of radius \(R\) and carrying a charge \(Q\).
4. Use Gauss law to find the electric field of two coaxial long cylindrical shells of radii \(a,b, a< b\), given that the charge per unit length on the shells is \(\pm \lambda\). Use electrostatic energy to find the capacitance per unit length of the system.
5. A uniformly charged solid sphere carries total charge \(Q\). Use stress tensor to compute the total force on northern hemisphere.