MODEL QUESTIONS (IPE PATTERN)

$ABC$ is an equilateral triangle of side $2 m$. There is a uniform electric field of intensity $100 V/m$ in the plane of the triangle and parallel to $BC$ as shown. If the potential at A is $200 V$, then the electric potentials at $B$ and $C$ are respectively.

An electric dipole of moment $p$ is placed in a uniform electric field $E$ with $p$ parallel to $E$. it is then rotated by an angle $q$. The work done is -

Three identical metal plates each of area $\mathrm{A}$ are arranged parallel to each other, $\mathrm{d}$ is the distance between the plates as shown. A battery of $\mathrm{V}$ volts is connected as shown. The charge stored in the system of plate is - 

Four identical metal plates each of area $A$ are separated mutually by a distance $d$ and are connected as shown. Find the capacity of the system between the terminal $A$ and $B$.

In the circuit shown the battery of $\mathrm{V}$ volt has no internal resistance. All three condensers are equal in capacity. Find the condenser that carries more charge?

Two capacitor A and B of capacities $C$ and $2C$ are connected in parallel and the combination of is connected to a battery of $V$ volts. After the charging is over, the battery is removed. Now a dielectric slab of $K = 2$ is inserted between the plates of A so as to fill the space completely. The energy lost by the system during the sharing of charges is ?

A condenser of certain capacity is charged to a potential V and stores some energy. A second condenser of twice the capacity is to store the half the energy of first, find to what potential one must be charged?

In a Van de Graaff type generator a spherical metal shell is to be a $15\times {10}^6 \mathrm{V}$ electrode. The dielectric strength of the gas surrounding the electrode is $5\times {10}^7 {\mathrm{Vm}}^{-1}$. What is the minimum radius (in centimetres)  of the spherical shell required?