Define electric potential and obtain an expression between intensity of electric field due to a point charge and electric potential. Also show that electric field is gradient of electric potential.

Figure shows three points $A,B$ and $C$ in a region of uniform electric Field $\overrightarrow{E}$. The line $AB$ is perpendicular and $BC$ is parallel to the field lines. Then which of the following hold good? ($V_A,V_B$ and $V_C$ represent the electric potential at points $A, B$ and $C$ respectively )

As shown in the figure below, a point charge $q$ moves from point $P$ to a point $S$ traversing a path $PQRS$ in a uniform $\overrightarrow{E}.$ The electric field is directed along a direction parallel to $x$-axis. The coordinates of, $P,Q,R$ and $S$ are $\left(a,b,0\right)\left(2a,0,0\right)\left(a,-b,0\right)$ and $\left(0,0,0\right)$ respectively. What is the work done by the field in the process?

A total charge $Q$ is uniformly distributed over a long rod $\mathrm{AB}$ of length $L$ as shown in the figure below. The electric potential at the point $\mathrm{O}$ lying at a distance $\frac{L}{2}$ from the end $\mathrm{A}$ is

Four capacitors with capacitances $C_1=1 \mathrm{\mu F},C_2=1.5 \mathrm{\mu F}$, $C_3=2.5 \mathrm{\mu F}$ and $C_4=0.5 \mathrm{\mu F}$ are connected as shown and are connected to a $30$ volt source. The potential difference between points $a$ and $b$ is:

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is :