Continuous charge distributions spread over a line, or a surface, or volume, are introduced. The electric field due to a continuous charge distribution is obtained by dividing the charge distributions into infinitesimal elements, and summing over electric fields due to the small elements. The computation can often be simplified by making use of symmetries of the problem.

Coulomb’s law is stated for electric field of a point particle. For several point charges the field is obtained as a vector sum of the fields of individual charges

The flux of electric field is defined and As a simple example, the flux of the electric field due to a point charge at the center of a sphere is explicitly computed. Other cases are briefly mentioned an statement of Gauss law is given.

We will call \(\vec B\) field as magnetic field when no medium is present.\\ In presence of a magnetic medium, \(\vec B\) will be called magnetic flux density or magnetic induction. The field \(vec H\) will called magnetic intensity or magnetic field intensity

A brief overview of how electric and magnetic fields produced.

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Find the electric field due to a uniformly charged hemisphere of radius \(R\) at the north pole.

Find the direction and magnitude of $\vec{E}$ at the center of a square with charges at the corners as shown in figure below. Assume that $ q= 1\times 10^{-8}$coul, $a=5$cm

Summary

The electric field is to be computed at a point $P$ on the axis of a thin cylindrical shell having uniform surface charge density $\sigma$. Divide 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 field as an integral.

Compute the integral for the cylindrical shell and show that the field due to the cylindrical shell is given by $$ E = \frac{Q}{4\pi\epsilon_0}\frac{1}{(b-a)}\left(\frac{1}{\sqrt{a^2+R^2}}-\frac{1}{\sqrt{ b^2+R^2}}\right) $$ where \(Q\) is the total charge on the cylinder.

The SI units in use in electromagnetic theory are explained and values of some important constants given.

Force on a hemisphere of a conducting shell in uniform electric field is computed and is shown to be

\[ F = \frac{9}{4}\pi \epsilon_0 R^2 E_0^2\]

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