A circle of radius $a$ has charge density given by $\lambda ={\lambda }_0{\cos }^2\theta$ on its circumference, where ${\lambda }_0$ is a positive constant and $\theta$ is the angular position of a point on the circle with respect to some reference line. The potential at the centre of the circle is

Four point charges $q_A=2 \mu C, q_B=-5 \mu C, q_C=2 \mu C, q_D=-5 \mu C$ are located at the corners of a square $ABCD$ of side $10 \mathrm{cm}.$ The force acting on a charge of $1 \mu \mathrm{C}$ placed at centre of the square is

Three charges are placed at the three vertices of an equilateral triangle of side $a$ as shown in the figure. The force experienced by the charge placed at the vertex $A$ in a direction normal to $BC$ is

Eleven equal point charges, all of them having a charge $+Q,$ are placed at all the hour positions of a circular clock of radius $r$ except at the $10 \mathrm{h}$ position. What is the electric field strength at the centre of the clock?

Shown in the figure is a shell made of a conductor. It has inner radius $a$ and outer radius $b$, and carries charge $Q$ . At its centre a dipole $\overrightarrow{\mathit{p}}$ is placed as shown then:

A uniformly charged solid sphere of radius R has potential $V_0$ (measured with respect to $\infty$ ) on its surface. For this sphere the equipotential surfaces with potential $\frac{3V_0}{2},\frac{5V_0}{4},\frac{3V_0}{4}$ and $\frac{V_0}{4}$ have radius $R_1$ , $R_2, R_3$ and $R_4$ respectively. Then

Note : This question had two option correct at the time of examination. Proper corrections are made in the question to avoid it.