If on the concentric hollow spheres of radii $r$ and $R( > r)$ the charge $Q$ is distributed such that their surface densities are same then the potential at their common centre is
$\frac{{Q\left( {{R^2} + {r^2}} \right)}}{{4\pi \varepsilon _0\left( {R + r} \right)}}$
$\frac{{QR}}{{R + r}}$
Zero
$\frac{{Q(R+r)}}{{4\pi \varepsilon _0\left( {{R^2} + {r^2}} \right)}}$
A thin spherical conducting shell of radius $R$ has charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $P$ at a distance $R/2$ from the centre of the shell is
Two concentric spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statement is
$(A)$ Charge on $B$ is zero
$(B)$ Potential at $B$ is zero
$(C)$ Charge is uniformly distributed on $A$
$(D)$ Charge is non uniformly distributed on $A$
Force between $A$ and $B$ is $F$. If $75\%$ charge of $A$ is transferred to $B$ then force between $A$ and $B$ is
If potential at centre of uniformaly charged ring is $V_0$ then electric field at its centre will be (assume radius $=R$)
Three charges $2q,\, - q,\, - q$ are located at the vertices of an equilateral triangle. At the centre of the triangle