An electric dipole is held in a uniform electric field. (i) Show that the net force acting on it is zero. (ii) The dipole is aligned parallel to the field. Find the work done in rotating it through the angle of 180°.

An electric dipole of length 4 cm, when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of $4{\sqrt{3}}$ Nm. Calculate the potential energy of the dipole, if it has charge ± 8 nC.

Find the expression for electric field intensity in an axial position due to electric dipole.

Two point charges q1 and q2 are located at $\stackrel{\rightarrow}{r₁}$ and $\stackrel{\rightarrow}{r₂}$ respectively in an external electric field E. Obtain the expression for the total work done in assembling this configuration.

Two point charges q1 and q2 are located at points (a, 0, 0) and (0, b, 0) respectively. Find the electric field due to both these charges at the point (0, 0, c).

A small metallic sphere carrying charge +Q is located at the centre of a spherical cavity in a large uncharged metallic spherical shell. Write the charges on the inner and outer surfaces of the shell. Write the expression for the electric field at the point P1.

A test charge q is moved without acceleration from A to C along the path from A to B and then from B to C in electric field E as shown in the figure.

An electric dipole is placed in a uniform electric field $\stackrel{\rightarrow}{E}$ with its dipole moment $\stackrel{\rightarrow}{p}$ parallel to the field. Find (i) the work done in turning the dipole till its dipole moment points in the direction opposite to $\stackrel{\rightarrow}{E}$ . (ii) the orientation of the dipole for which the torque acting on it becomes maximum.

Find the P.E. associated with a charge q if it were present at the point P with respect to the ‘setup’ of two charged spheres, arranged as shown. Here O is the mid-point of the line O1O2.

Five charges, q each are placed at the corners of a regular pentagon of side a. (i) What will be the electric field at O if the charge from one of the corners (say A) is removed ? (ii) What will be the electric field at O if the charge q at A is replaced by - q ?

N spherical droplets, each of radius r, have been charged to have a potential V each. If all these droplets were to coalesce to form a single large drop, what would be the potential of this large drop ? (It is given that the capacitance of a sphere of radius x equals $4\pi\varepsilon_{0}k r.)$

Three concentric metallic shells A, B and C of radii a, b and c (a < b < c) have surface charge densities +σ, –σ and +σ respectively as shown in the figure.

Two charges q and –3q are placed on x-axis separated by distance d. Where a third charge 2q should be placed such that it will not experience any force ?

Two closely spaced equipotential surfaces A and B with potentials V and V + $\delta V$, (where $\delta V$ is the change in V), are kept $\delta l$ distance apart as shown in the figure. Deduce the relation between the electric field and the potential gradient between them. Write the two important conclusions concerning the relation between the electric field and electric potentials.

Two point charges q and –2q are kept d distance apart. Find the location of the point relative to charge q at which potential due to this system of charges is zero.