In the circuit shown, a potential difference of $60\,V$ is applied across $AB$. The potential difference between the point $M$ and $N$ is.....$V$

A hollow metal sphere of radius $5\, cm$ is charged so that the potential on its surface is $10\, V$. The potential at the centre of the sphere is.....$V$

In a parallel plate air capacitor, a cathode beam comprising $n = 10^6$ electrons is emitted with a velocity $v_0 = 10^8\ m/s$ into the space between the plates. The potential difference between the plate is $\phi  = 400\ V$ ,the seperation between the plates is $d = 2\ cm$ and the area of each plate is $l^2 = 100\ cm^2$ . The deflection of the electron beam, is ........... $mm$

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

Charge $q$ is uniformly distributed over a thin half ring of radius $R$. The electric field at the centre  of the ring is 

A point charge $q$ is placed at a distance $\frac{a}{2}$ directly above the centre of a  square of side $a$ . The electric flux through the square is