When a charge of $3 \, C$ is placed in a uniform electric field, it experiences a force of $3000 \, N$. Within this field, the potential difference between two points separated by a distance of $1 \, cm$ is: (in $V$)

For a charged spherical ball,electrostatic potential inside the ball varies with $r$ as $V = 2ar^2 + b$. Here,$a$ and $b$ are constants and $r$ is the distance from the center. The volume charge density inside the ball is $-\lambda a \varepsilon$. The value of $\lambda$ is $...........$. $\varepsilon =$ permittivity of medium.

$A$ uniform electric field of $20\, N/C$ exists along the $x$-axis in a space. The potential difference $(V_B - V_A)$ for the points $A(4\,m, 2\,m)$ and $B(6\,m, 5\,m)$ is.....$V$.

Electric field in a region is given by $\vec{E} = Ax\hat{i} + By\hat{j}$, where $A = 10 \ V/m^2$ and $B = 5 \ V/m^2$. If the electric potential at a point $(10, 20)$ is $500 \ V$, then the electric potential at the origin is . . . . . . $V$.

Write the relation between electric field and electrostatic potential.

Potential in the $x-y$ plane is given as $V = 5(x^2 + xy) \, V$. The electric field at the point $(1, -2)$ will be