Four point charges $-Q, -q, 2q$ and $2Q$ are placed, one at each comer of the square. The relation between $Q$ and $q$ for which the potential at the centre of the square is zero is

Consider a thin spherical shell of radius $R$ with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $|\vec{E}(r)|$ and the electric potential $V(r)$ with the distance r from the centre, is best represented by which graph?

Ten charges are placed on the circumference of a circle of radius $R$ with constant angular separation between successive charges. Alternate charges $1,3,5,7,9$ have charge $(+q)$ each, while $2,4,6,8,10$ have charge $(-q)$ each. The potential $V$ and the electric field $E$ at the centre of the circle are respectively

(Take $V =0$ at infinity $)$

Consider two conducting spheres of radii ${{\rm{R}}_1}$ and ${{\rm{R}}_2}$ with $\left( {{{\rm{R}}_1} > {{\rm{R}}_2}} \right)$. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.

The radius of nucleus of silver (atomic number $=$ $47$) is $3.4 \times {10^{ – 14}}\,m$. The electric potential on the surface of nucleus is $(e = 1.6 \times {10^{ – 19}}\,C)$