[2018EM/HMW-01]

$ \newcommand {\pieps}{4 \pi \epsilon_0} $

2018 Electromagnetic Theory ---- Table of Contents

Electrodynamics                                                                      Aug 10, 2018

Tutorial I

• The electric field is to be computed at a point $P$ on the axis of a thin cylindrical shell having uniform surface charge density $\sigma$. Dividing the shell by planes perpendicular to the axis, and using the expression for a electric field due to a uniformly charged ring, write expressions for the electric field as an integral. Compute the integral for the cylindrical shell and show that the field due to the cylindrical shell is given by $$ E = \frac{Q}{\pieps}\frac{1}{(b-a)}\left(\frac{1}{\sqrt{a^2+R^2}}-\frac{1}{\sqrt{ b^2+R^2}}\right) $$ 
• Sixteen equal charges, \(q\), are placed on vertices of a regular polygon of seventeen sides. Find the electric field at the centre of the polygon.
• Two solid spheres, each having a radius \(R\), have uniform charge densities \(+\rho\) and \(-\rho\) and are kept at a distance \(d < 2R\) apart. Show that the electric field in the overlap region is constant.
• A conical shell of height \(h\) and radius of the base \(a\) carries a uniform surface charge density \(\sigma\). Compute the potential difference between the vertex and the center of the base.