The potential at any observation point P of a static electric field is defined as the work done by the external agent (or negative of work done by electrostatic field) in slowly bringing a unit positive point charge from infinity to the observation point. Figure shows the potential variation along the line of charges. Two point charges Q₁ and Q₂ lie along a line at a distance from each other.

(i) At which of the points 1, 2 and 3 is the electric field is zero?

(ii) The signs of charges Q₁ and Q₂ respectively are

(iii) Which of the two charges Q₁ and Q₂ is greater in magnitude?

(iv) Which of the following statement is not true?

(v) Positive and negative point charges of equal magnitude are kept at \(\left(0,0, \frac{a}{2}\right)\) and \(\left(0,0, \frac{-a}{2}\right)\) respectively.
The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is

For the various charge systems, we represent equipotential surfaces by curves and line of force by full line curves. Between any two adjacent equipotential surfaces, we assume a constant potential difference the equipotential surfaces of a single point charge are concentric spherical shells with their centres at the point charge. As the lines of force point radially outwards, so they are perpendicular to the equipotential surfaces at all points.

(i) Identify the wrong statement.

(ii) Nature of equipotential surface for a point charge is

(iii) A spherical equipotential surface is not possible

(iv) The work done in carrying a charge q once round a circle of radius a with a charge Q at its centre is

(v) The work done to move a unit charge along an equipotential surface from P to Q

The electrical capacitance of a conductor is the measure of its ability to hold electric charge. An isolated spherical conductor of radius R. The charge Q is uniformly distributed over its entire surface. It can be assumed to be concentrated at the centre of the sphere. The potential atany point on the surface of the spherical conductor will be \(V=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{R}\).

Capacitance of the spherical conductor situated in vacuum is \(C=\frac{Q}{V}=\frac{Q}{\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{R}} \text { or } C=4 \pi \varepsilon_{0} R\) Clearly, the capacitance of a spherical conductor is proportional to its radius.
The radius of the spherical conductor of 1F capacitance is R = \(\frac{1}{4 \pi \varepsilon_{0}}\). C and this radius is about 1500 times the radius of the earth \(\left(\sim 6 \times 10^{3} \mathrm{~km}\right)\).
(i) If an isolated sphere has a capacitance 50pF. Then radius is

(ii) How much charge should be placed on a capacitance of 25 pF to raise its potential to l0⁵ V?

(iii) Dimensions of capacitance is

(iv) Metallic sphere of radius R is charged to potential V. Then charge q is proportional to

(v) If 64 identical spheres of charge q and capacitance C each are combined to form a large sphere. The charge and capacitance of the large sphere is

A dielectric slab is a substance which does not allow the flow of charges through it but permits them to exert electrostatic forces on one another.
When a dielectric slab is placed between the plates, the field E_o polarises the dielectric. This induces charge -Q_p on the upper surface and + Q_p on the lower surface of the dielectric. These induced charges set up a field E_p inside the dielectric in the opposite direction of \(\vec{E}_{0}\) as shown.

(I) In a parallel plate capacitor, the capacitance increases from \(4 \mu \mathrm{F}\) to 80\(\mu \mathrm{F}\) on introducing a dielectric medium between the plates. What is the dielectric constant of the medium?

(ii) A parallel plate capacitor with air between the plates has a capacitance of 8 pF. The separation between the plates is now reduced half and the space between them is filled with a medium of dielectric constant 5.
Calculate the value of capacitance of the capacitor in second case.

(iii) A dielectric introduced between the plates of a parallel plate condenser

(iv) A parallel plate capacitor of capacitance 1 pF has separation between the plates is d. When the distance of separation becomes 2d and wax of dielectric constant x is inserted in it the capacitance becomes 2 pF. What is the value of x?

(v) A parallel plate capacitor having area A and separated by distance d is filled by copper plate of thickness b. The new capacity is

When an insulator is placed in an external field, the dipoles become aligned. Induced surface charges on the insulator establish a polarization field \(\vec{E}_{i}\) in its interior. The net field \(\vec{E}\) in the insulator is the vector sum of \(\vec{E}_{0}\) and \(\vec{E}_{i}\) as shown in the figure.

On the application of external electric field, the effect of aligning the electric dipoles in the insulator is called polarisation and the field \(\vec{E}_{i}\) is known as the polarisation field.
The dipole moment per unit volume of the dielectric is known as polarisation \((\vec{P})\).
For linear isotropic dielectrics, \(\vec{P}=\chi \vec{E}\) where X = electrical susceptibility of the dielectric medium.
(i) Which among the following is an example of polar molecule?

(ii) When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance

(iii) Which of the following is a dielectric?

(iv) For a polar molecule, which of the following statements is true?

(v) When a comb rubbed with dry hair attracts pieces of paper. This is because the