$A$ spherical shell of radius $6 \ cm$ is placed concentrically with a sphere of radius $4 \ cm$. The outer spherical shell is grounded. If the potential of the inner sphere is $3 \ e.s.u.$,what is the charge on it in $e.s.u.$?

What physical quantities may $X$ and $Y$ represent? ($Y$ represents the first mentioned quantity)

$(a)$ Determine the electrostatic potential energy of a system consisting of two charges $7 \; \mu C$ and $-2 \; \mu C$ (with no external field) placed at $(-9 \; cm, 0, 0)$ and $(9 \; cm, 0, 0)$ respectively.
$(b)$ How much work is required to separate the two charges infinitely away from each other?
$(c)$ Suppose that the same system of charges is now placed in an external electric field $E = A(1/r^2)$; $A = 9 \times 10^5 \; C \cdot m^{-2}$. What would the electrostatic energy of the configuration be?

$A$ parallel plate capacitor is charged by connecting it to a battery. The battery is disconnected and the plates of the capacitor are pulled apart to make the separation between the plates twice. Again the capacitor is connected to the battery (with same polarity) then

An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by the above two particles will be:

$A$ parallel plate capacitor has capacitance $C$. If the charges on the plates are $Q$ and $-3Q$,find the potential difference between the plates.