## Class 12 - Physics

#### Electrostatic Potential and Capacitance

**Question:**

**Answer:**

## Questions and Answers

**Electrostatic Potential and Capacitance**- Questions

For any charge configuration,equipotential surface through a point is a normal to the electric field. Justify. [Delhi 2014]

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.

(i)Calculate the potential difference between A and C.

(ii)At which point (of the two) is the electric potential more and why?

Two point charges 40, O are separated by lm in air. At what point on the line joining the charges, is the electric field intensity zero? Also calculate the electrostatic potential energy of the system of charges taking the value of charge, O = 2 X 10~^{7} C. [All India 2008]

Two point charges 40, O are separated by lm in air. At what point on the line joining the charges, is the electric field intensity zero? Also calculate the electrostatic potential energy of the system of charges taking the value of charge, O = 2 X 10~^{7} C. [All India 2008]

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

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

S_{1 }: At any point inside the sphere, electric intensity is zero.

S_{2}: At any point inside the sphere, the electrostatic potential is 100 V.

Which of the following is a correct statement?

(a) S_{1} is true but S_{2} is false

(b) Both S_{1} and S_{2} are false

(c) S_{1} is true, S_{2} is also true and 5, is the cause of S_{2}

(d) S_{2} is true, S_{2} is also true but the statements are independent

Equipotentials 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

Equipotentials 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

A parallel plate capacitor is connected to a battery as shown in figure. Consider two situations.

A. Key K is kept closed and plates of capacitors are moved apart using insulating handle.

B. Key K is opened and plates of capacitors are moved apart using insulating handle.

Choose the correct option(s).

(a) In A, Q remains the same but G changes

(b) In B, V remains the same but C changes

(c) In A, V remains the same hence Q changes

(d) In B ,Q remains the same hence V changes

A test charge q is made to move in the electric field of a point charge Q along two different closed paths [figure first path has sections along and perpendicular to lines of electric field]. Second path is a rectangular loop of the same area as the first loop. How does the work done compare in the two cases?

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

Two parallel plate capacitors of capacitances C_{x} and C_{2} such that C_{x} =2C_{2} are connected across a battery of V volt as shown in the figure Initially, the key (k) is kept closed to fully charge the capacitors.The key is now thrown open and a dielectric slab of dielectric constant K is inserted in the two capacitors to completely fill the gap between the plates. Find the ratio of (i) the net capacitance and (ii) the energies stored in the combination before and after the introduction of the dielectric slab.[Delhi 2014 C]

What is the electric potential due to an electric dipole at an equatorial point?[All India 2009]

A dipole with its charge -q and +q located at the points (0, – b,0) and (0,+ 5,0) is present in a uniform electric field E. The equipotential surfaces of this field are planes parallel to the Y Z-plane.

(i)What is the direction of the electric field E?

(ii)How much torque would the dipole experience in this field?[Delhi 2010 C]

(i)Can two equipotential surfaces intersect each other? Give reasons,

(ii)Two charges – qand + qare located at points A (0, 0, – a) and B{0, 0, +a) respectively. How much work is done in moving a test charge from point P{7, 0, 0) to Q(- 3, 0, 0)? [Delhi 2009]

(i)Write two characteristics of equipotential surfaces.

(ii) Draw the equipotential surfaces due to an electric dipole. [All India 2009 C]

A wire AB is carrying a steady current of 12 A and is lying on the table. Another wire CD carrying 5 A is held directly above AB at a height of 1mm. Find the mass per unit length of the wire CD, so that it remains suspended at its position when left free. Give the direction of the current flowing in CD with respect to that in [Take the value of g =10 ms^{-2}][All India 2013]

In the circuit shown in figure initially key K_{1}

is closed and key K_{2} is open. Then K_{1} is opened and K_{2} is closed (order is important).

[Take Q’_{1} and Q’_{2} as charges on C_{1} and C_{2} and V_{1} and V_{2} as voltage respectively.]

Then, E

(a) charge on C, gets redistributed such that V_{1} = V_{2}

(b) charge on C_{1} gets redistributed such that Q’_{1} = Q’_{2}

(c) charge on C_{1} gets redistributed such that C_{1}V_{1} + C_{2}V_{2} = C_{1}E

(d) charge on C_{1} gets redistributed such that Q’_{1} + Q’_{2}=Q

In the circuit shown in figure initially key K_{1}

is closed and key K_{2} is open. Then K_{1} is opened and K_{2} is closed (order is important).

[Take Q’_{1} and Q’_{2} as charges on C_{1} and C_{2} and V_{1} and V_{2} as voltage respectively.]

Then, E

(a) charge on C, gets redistributed such that V_{1} = V_{2}

(b) charge on C_{1} gets redistributed such that Q’_{1} = Q’_{2}

(c) charge on C_{1} gets redistributed such that C_{1}V_{1} + C_{2}V_{2} = C_{1}E

(d) charge on C_{1} gets redistributed such that Q’_{1} + Q’_{2}=Q

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.

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.

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)?

A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as Îµ= Î±U where Î± = 2V^{-1}. A similar capacitor with no dielectric is charged to U_{0} = 78 V. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.

A capacitor is made of two circular plates of radius R each, separated by a , distance d << R. The capacitor is connected to a constant voltage. A thin

conducting disc of radius r << R and thickness t << r is placed at the centre of the bottom plate. Find the minimum voltage required to lift the disc if the mass of the disc is m.

(a) In a quark model of elementary particles, a neutron is made of one up quarks [charge (2/3)e] and two down quarks [charges (-l/3)e]. Assume that they have a triangle configuration with side length of the order of 10^{-15 }m. Calculate electrostatic potential energy of neutron and compare it with its mass 939 MeV.

(b) Repeat above exercise for a proton which is made of two up and one down quark.

Two metal spheres, one of radius R and the other of radius 2R, both have same surface charge density Ïƒ. They are brought in contact and separated. What will be the new surface charge densities on them?

The given graph shows the variation of charge q versus potential difference V for two capacitors C_{l} and C_{2}. Both the capacitors” have same plate separation but plate area of C_{2 }is greater than that C_{x} .Which line (A or B) corresponds to and why?[All India 2014 C]

The following graph shows the variation of charge Q with voltage V for two capacitors K and L In which capacitor is more electrostatic energy stored?

A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.[All India 2014]

Two identical parallel plate (air) capacitors C_{x} and C_{2} have capacitance C each. The space between their plates is now filled with dielectrics as shown in the figure. If the two capacitors still have equal capacitance, they obtain the relation between dielectric constants K, K_{x }andK_{2}.[Foreign 2011]

Figure shows a sheet of aluminium foil of negligible thickness placed between the plates of a capacitor. How will its capacitance be affected if

(i)the foil is electrically insulated?

(ii)the foil is connected to the upper plate with a conducting wire?[Foreign 2011]

(i)Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor.

(ii) The electric field inside a parallel plate capacitor is E. Find the amount of work done in moving a charge q over a closed rectangular loop abcda. [Delhi 2014]

A capacitor of 200 pF is charged by a 300 V battery. The battery is then disconnected and the charged capacitor is connected to another uncharged capacitor of 100 pF. Calculate the difference between the final energy stored in the combined system and the initial energy stored in the single capacitor.[Foreign 2012]

A parallel plate capacitor, each with plate area A and separation d is charged to a potential difference V. The battery used to charge it remains connected. A dielectric slab of thickness d and dielectric constant K is now placed between the plates. What change if any will take place in

(i)charge on plates?

(ii)electric field intensity between the plates?

(iii)capacitance of the capacitor? Justify your answer in each case.[Delhi 2010]

(i) How is the electric field due to a charged parallel plate capacitor affected when a dielectric slab is inserted between the plates fully occupying the intervening region?

(ii) A slab of material of dielectric constant K has the same area as the plates of a parallel plate capacitor but has thickness 1/2 d,

where d is the separation between the plates. Find the expression for the capacitance when the slab is inserted between the plates. [Foreign 2010]

(i) Plot a graph comparing the variation of potential V and electric field E due to a point charge 0 as a function of distance R from the point charge.

(ii) Find the ratio of the potential differences that must be applied across the parallel and the series

combination of two capacitors, C_{l }and C_{2} with their capacitances in the ratio 1 : 2, so that the energy stored in the two cases becomes the same[Foreign 2010]

A parallel plate* capacitor is charged by a battery. After sometime, the battery is disconnected and a dielectric slab of dielectric constant K is inserted between the plates. How would

(i)the electric field between the plates

(ii)the energy stored in the capacitor be affected? Justify your answer. [All India 2009]