A charge $$Q$$ is placed at a distance $$a/2$$ above the center of the square surface of edge a as shown in the figure.


The electric flux through the square surface is

Four closed surfaces and corresponding charge distributions are shown below.



Let the respective electric fluxes through the surfaces be $${\Phi _1},$$ $${\Phi _2},$$ $${\Phi _3}$$ and $${\Phi _4}$$. Then :

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $$P,$$ in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60^o with the direction of the field ?

An electric dipole has a fixed dipole moment $$\overrightarrow p $$, which makes angle $$\theta$$ with respect to x-axis. When subjected to an electric field $$\mathop {{E_1}}\limits^ \to = E\widehat i$$ , it experiences a torque $$\overrightarrow {{T_1}} = \tau \widehat k$$ . When subjected to another electric field $$\mathop {{E_2}}\limits^ \to = \sqrt 3 {E_1}\widehat j$$ it experiences a torque $$\mathop {{T_2}}\limits^ \to = \mathop { - {T_1}}\limits^ \to $$ . The angle $$\theta$$ is: