In a region, if electric field is defined as $\vec E = \left( {\hat i + 2\hat j + \hat k} \right)\,V/m$ , then the potential difference between two points $A (0, 0, 0)$ and $B (2, 3, 4)$ in that region, is ......$V$

Assertion : Two concentric charged shells are given. The potential difference between the shells depends on charge of inner shell.

Reason : Potential due to charge of outer shell remains same at every point inside the sphere.

Two charges $3 \times 10^{-8}\; C$ and $-2 \times 10^{-8}\; C$ are located $15 \;cm$ apart. At what point on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

Assume that an electric field $\overrightarrow E  = 30{x^2}\hat i$ exists in space. Then the potential difference $V_A -V_O$, where $V_O$ is the potential at the origin and $V_A$ the potential at $x = 2\, m$ is

Derive an expression for the electric potential in a electric field of positive point charge at distance $\mathrm{r}$.

The electric field in a region surrounding the origin is uniform and along the $x$ - axis. A small circle is drawn with the centre at the origin cutting the axes at points $A, B, C, D$ having co-ordinates $(a, 0), (0, a), (-a, 0), (0, -a)$; respectively as shown in figure then potential in minimum at the point