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An isolated metal sphere of radius $r$ is given a charge $q$. The potential energy of the sphere is :

Two charges of $10μC$* *and $−20μC$* *are separated by a distance of $20cm$. The distance of the point from smaller charge where electric potential is zero if it lies between them is :

A cloud carries a charge of 1000*C *at a potential of 5 kV. If the cloud discharge, the amount of energy released:

Write the definition of electric potential. Calculate the electric potential due to a point charge Q at a distance r from it. Draw a graph between electric potential V and distance r for a point charge Q.

A neutral hydrogen molecule has two protons and two electrons. If one of the electrons is removed we get a hydrogen molecular ion $(H_{2})$ . In the ground state of $H_{2}$ the two protons are separated by roughly $1.5$$A_{o}$ and the electrons is roughly $1$ $A_{o}$ from each proton. The potential energy of the system is :

The electric potential difference between the ground and a cloud in a particular thunderstorm is $1.2×10_{9}V$. What is the magnitude of the change in energy(in multiples of the $eV$) of an electron that moves between the ground and the cloud?

A parallel plate capacitor is to be designed with a voltage rating 1 kV, using a material of dielectric constant 3 and dielectric strength about $10_{7}Vm_{−1}$. (Dielectric strength is the maximum electric field a material can tolerate without breakdown, i.e., without starting to conduct electricity through partial ionisation.) For safety, we should like the field never to exceed, say 10% of the dielectric strength.What minimum area of the plates is required to have a capacitance of 50 pF ?

A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of $2.5μC$. The space between the concentric spheres is filled with a liquid of dielectric constant 32.

(a) Determine the capacitance of the capacitor.

(b) What is the potential of the inner sphere?

(c) Compare
the capacitance of this capacitor with that of an isolated
sphere of radius 12 cm. Explain why the latter is much smaller.

(a) Obtain a relation for equivalent capacitance of the series combination of capacitors. Draw a circuit diagram.

(b) $10$ capacitors each of capacity $10μF$ are joined first in series and then in parallel. Write the value of product of equivalent capacitances.

(c) What will be the value of capacitance of a $4μF$ capacitor if a dielectric of dielectric constant $2$ is inserted fully between the plates of parallel plate capacitor.

(b) $10$ capacitors each of capacity $10μF$ are joined first in series and then in parallel. Write the value of product of equivalent capacitances.

(c) What will be the value of capacitance of a $4μF$ capacitor if a dielectric of dielectric constant $2$ is inserted fully between the plates of parallel plate capacitor.

Show that the force on each plate of a parallel plate capacitor has a magnitude equal to $(21 )$ QE, where Q is the charge on the capacitor, and E is the magnitude of electric field between the plates. Explain the origin of the factor .