The electric field in a region is given by: $\overrightarrow{E}=\left(4axy\sqrt{z}\right)\hat{i}+\left(2a{x}^2\sqrt{z}\right)\hat{j}+\left(\frac{a{x}^{2}y}{\sqrt{z}}\right)\hat{k}$ , where $a$ is a positive constant. The equation of an equipotential surface will be of the form

Q. A particle in a certain consevative force field has a potential energy given by $U=\frac{20xy}{z}$. The force exerted on it is

Q. Assertion :The electrostatic force on a charged particle located on an equipotential surface is zero. Reason: $x$ component of electric field is given by, $E_x=-\frac{\delta V}{\delta x}$ and on equipotential surface potential $V$ is constant.

Q. 1) For equipotential surfaces the following statement is correct or not:

A) Equipotential surfaces are closer in regions of large electric fields compared to regions of lower electric fields

2) For equipotential surfaces the following statement is correct or not:

B) Equipotential surfaces will be more crowded near sharp edges of a conductor

3) For equipotential surfaces the following statement is correct or not:

C) Equipotential surfaces will be more crowded near regions of large charge densities

4) For equipotential surfaces the following statement is correct or not:

D) Equipotential surfaces will always be equally spaced

Q. Define an equipotential surface. Draw equipotential surfaces :

(i) in the case of a single point charge and
(ii) in a constant electric field in Z-direction.

Why the equipotential surfaces about a single charge are not equidistant ?
(iii) Can electric field exist tangential to an equipotential surface ? Give reason.

Q.

The electric potential in a certain region of space is given by $v=-3x^2+4x$, where x is in metres and v is in volts. In this region, the equipotential surfaces are