Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Electrostatics, Exercise 3: Competitive Thinking

A charge $Q$ is uniformly distributed over a long rod $A B$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at a distance $L$ from the end $A$ is

The region between two concentric spheres of radii $a$ and $b$, respectively (see figure), has volume charge density $\rho=\frac{A}{r},$ where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge $Q$. The value of $A$ such that the electric field in the region between the spheres will be constant, is:

Two capacitors $C_1$ and $C_2$ are charged to $120 \mathrm{V}$ and $200 \mathrm{V}$, respectively. It is found that by connecting them together, the potential on each one can be made zero. Then 

The radius of earth is $6400 \mathrm{km}$. Its capacitance will be

The capacity of an isolated sphere of radius $9 \mathrm{cm}$ is $C$. When it is connected to an earthed concentric thin hollow sphere of radius $R$, the capacity becomes $10C$. Then the value of $R$ is

Assertion: A parallel plate capacitor is connected across battery through a key. A dielectric slab of constant $k$ is introduced between the plates. The energy which is stored becomes $k$ times.

Reason: The surface density of charge on the plate remains constant or unchanged.

Assertion: The lightning conductor at the top of the high building has sharp pointed ends.

Reason: The surface density of charge at sharp points is very high resulting in the setting up of electric wind.

Putting a dielectric substance between two plates of condenser: capacity, potential and potential energy, respectively