Assignment

When an electric dipole having dipole moment $\overrightarrow{p}$ is placed in an uniform electric field $\overrightarrow{E}$, the torque $\overrightarrow{\tau }$ acting on the dipole is

Three charges are placed on the vertices of an equilateral triangle of side length $I.$ Find the sign and magnitude of charge $q$ placed at centroid so that system of charges will be in equilibrium.

Write two basic properties of charge.

What is the relation between electric field intensity and the force ? What determines the direction of the force in an electric field ?

Electric field in the given figure is directed along $+ x$ direction and given by $E=50 x+10,$ where $E$ is in $N{C}^{-1}$ and $x$ is in meter. Calculate, (i) the electric flux through the cube (ii) the net charge enclosed within the cube

Define the term electric dipole moment, and derive an expression for electric field intensity due to a dipole on its axial line.

Derive an expression for the magnitude of electric field intensity at any point along the equatorial line of a short electric dipole. Give the direction of intensity at that point. For a short dipole what is the ratio of magnitude of electric field intensities at two equidistant points from the centre of dipole, one along the axial line and another on the equatorial line ?

(i) State Gauss's law in electrostatics and express it mathematically. Using it derive an expression for electric field at a point near a thin infinite plane sheet of electric charge.
(ii) Two plane sheets of charge having charge densities ${\mathrm{\sigma }}_1$ and ${\mathrm{\sigma }}_2$ are normal to each other. What will be the magnitude of electric field at point $O ?$