Electrostatic Potential and Capacitance

A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness d₁and dielectric constant K₁ and the other has thickness d₂ and dielectric constant K₂ as shown in figure. This arrangement can be thought as a dielectric slab of thickness d (= d₁ + d₂) and effective dielectric constant K. Then K is

Equipotential at a great distance from a collection of charges whose total sum is not zero are approximately

(a) Spheres                     

(b) Planes

(c) Paraboloids               

(d) Ellipsoids

The electrostatic potentiaLon the surface of a charged conducting sphere is 100 V. Two statements are made in this regard.

S₁ : At any point inside the sphere, electric intensity is zero.

S₂: At any point inside the sphere, the electrostatic potential is 100 V.

Which of the following is a correct statement?

(a) S₁is true but S₂ is false

(b) Both S₁ and S₂ are false

(c) S₁ is true, S₂ is also true and S₁, is the cause of S₂

(d) S₂ is true, S₂ is also true but the statements are independent

Figure shows some equipotential lines distributed in space. A charged object is moved from point A to point B.

(a) The work done in Fig. (i) is the greatest

(b) The work done in Fig. (ii) is least

(c) The work done is the same in Fig. (i), Fig.(ii) and Fig. (iii)

(d) The work done in Fig. (iii) is greater than Fig. (ii) but equal to that in

A positively charged particle is released from rest in an uniform electric field. The electric potential energy of the charge

(a) Remains a constant because the electric field is uniform

(b) Increases because the charge moves along the electric field

(c) Decreases because the charge moves along the electric field

(d) Decreases because the charge moves opposite to the electric field

A capacitor of 4 μF is connected as shown in the circuit. The internal resistance of the battery is 0.5 ?. The amount of charge on the capacitor plates will be

(a) 0                         

(b) 4 μC

(c) 16 μC                   

(d) 8 μC

Calculate the potential on the axis of a ring due to charge Q uniformly distributed along the ring of radius R.

Calculate potential energy of a point charge -q placed along the axis due to a charge +Q uniformly distributed along a ring of radius R. Sketch PE, as a function of axial distance z from the centre of the ring. Looking at graph, can you see what would happen if -q is displaced slightly from the centre of the ring (along the axis)?

Prove that, if an insulated, uncharged conductor is placed near a charged conductor and no other conductors are present, the uncharged body must intermediate in potential between that of the charged body and that of infinity.

A capacitor has some dielectric between its plates and the capacitor is connected to a DC source. The battery is now disconnected and then the dielectric is removed. State whether the capacitance, the energy stored in it, electric field, charge stored and the voltage will increase, decrease or remain constant.