A uniform surface charge of density $\sigma$ is given to a quarter of a disc extending up to infinity in the first quadrant of $x-y$ plane. The centre of the disc is at the origin $O$. Find the $z$-component of the electric field at the point $\left(0,0,z\right)$ and the potential difference between the points $\left(0,0,d\right)$ and $\left(0,0,2d\right)$.

  

Electric potential is given by $V=6x-8x{y}^2-8y+6yz-4z^2$. The electric force acting on $2 \mathrm{C}$ point charge placed on origin will be?

The figure gives the electric potential $V$ as a function of distance through five regions on $x‐$axis. Which of the following is true for the electric field $E$ in these regions?

Figure shows a charged conductor resting on an insulating stand. If at the point $P$ the charge density is $\sigma$, the potential is $V$ and the electric field strength is $E$, what are the values of these quantities at point $Q$?

The electrostatic potential on the surface of a charged conducting sphere is $100 \mathrm{V}$. Two statements are made in this regard
$S_1:$ at any point inside the sphere, the electric field intensity is zero.
$S_2:$ at any point inside the sphere, the electrostatic potential is $100 \mathrm{V}$.

Which of the following is a correct statement?