Physics

Electrostatic Potential and Capacitance

Question:

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

Answer:

(a) The collection of charges, whose total sum is not zero, with regard to great distance can be considered as a single point charge. The equipotential surfaces due to a point charge are spherical.
Important point:
The electric potential due to point charge q is given by V=q/4πϵ0r
It means electric potential due to point charge is same for all equidistant points. The locus of these equidistant points, which are at same potential, form spherical surface.

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Electrostatic Potential and Capacitance

Q 1.

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.  

Q 2.

Find the ratio of the potential differences that must be applied across the parallel and the series combination of two identical capacitors so that the energy stored in the two cases becomes the same.
[Foreign 2010]

Q 3.

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

ncert-exemplar-problems-class-12-physics-electrostatic-potential-and-capacitance-15

Q 4.

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]

Q 5.

The given graph shows the variation of charge q versus potential difference V for two capacitors Cl and C2. Both the capacitors” have same plate separation but plate area of C2 is greater than that Cx .Which line (A or B) corresponds to and why?[All India 2014 C]
important-questions-for-class-12-physics-cbse-capactiance-t-22-10

Q 6.

(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.

Q 7.

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]

Q 8.

If a conductor has a potential V≠0 and there are no charges anywhere else outside, then  
(a) there must be charges on the surface or inside itself
(b) there cannot be any charge in the body of the conductor
(c) there must be charges only on the surface
(d) there must be charges inside the surface

Q 9.

Define the term potential energy for charge q at a distance r in an external  field.  [All India 2009]

Q 10.

Find the charge on the capacitor as Shown in the circuit. [Foreign 2014]
important-questions-for-class-12-physics-cbse-capactiance-t-22-15

Q 11.

A capacitor of 4 μF is connected as shown in the circuit. The internal resistance of the battery is 0.5 Ω. The amount of charge on the capacitor plates will be
(a) 0 (b) 4 μC
(c) 16 μC (d) 8 μC

ncert-exemplar-problems-class-12-physics-electrostatic-potential-and-capacitance-1

Q 12.

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]

Q 13.

Name the physical quantity whose SI  unit is J/C. Is it a scalar or a vector quantity? [All India 2010]

Q 14.

Find the charge on the capacitor as Shown in the circuit. [Foreign 2014]
important-questions-for-class-12-physics-cbse-capactiance-t-22-15

Q 15.

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

Q 16.

(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.

Q 17.

Find the charge on the capacitor as Shown in the circuit. [Foreign 2014]
important-questions-for-class-12-physics-cbse-capactiance-t-22-15

Q 18.

important-questions-for-class-12-physics-cbse-capactiance-t-22-30

Q 19.

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

Q 20.

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

ncert-exemplar-problems-class-12-physics-electrostatic-potential-and-capacitance-15

Q 21.

Graph the electric potential (V) with distance r due to a point charge Q.[Delhi 2012]

Q 22.

A metal plate is introduced between the plates of a charged parallel plate capacitor. What is its effect on the capacitance of the capacitor?[Foreign 2009]

Q 23.

Why there is no work done in  moving a charge from one point to another on an equipotential surface?           [Foreign 2012]

Q 24.

Draw three equipotential surfaces  corresponding to a field that uniformly increases in magnitude but remains constant  along  Z-direction. How are  these  surfaces different from that of a constant electric field along  Z-direction? [Foreign 2008; All imiia 2009]

Q 25.

Consider a uniform electric field in the z -direction. The potential is a constant
(a) in all space (b) for any x for a given z
(c) for any y for a given z (d) on the x-y plane for a given z

Q 26.

In a region of constant potential
(a) the electric field is uniform
(b) the electric field is zero
(c) there can be no charge inside the region
(d) the electric field shall necessarily change if a charge is placed outside the region

Q 27.

Prove that a closed equipptential surface with no charge within itself must enclose an equipotential volume.

Q 28.

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

Q 29.

A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as  Îµ= αU where α  = 2V-1. A similar capacitor with no dielectric is charged to U0  = 78 V. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.

Q 30.

Two point charges q1 and q2 are located at q and r2, respectively in an external electric field E. Obtain the expression for the total work done in assembling this configuration. [Delhi 2014 C]

Q 31.

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

Q 32.

In the circuit shown in figure initially key K1  
is closed and key K2 is open. Then K1 is opened and K2 is closed (order is important).
[Take Q’1 and Q’2 as charges on C1 and C2 and V1 and V2 as voltage respectively.]
Then, E
(a) charge on C, gets redistributed such that V1 = V2
(b) charge on C1 gets redistributed such that Q’1 = Q’2
(c) charge on C1 gets redistributed such that C1V1 + C2V2 = C1E
(d) charge on C1 gets redistributed such that Q’1 + Q’2=Q

ncert-exemplar-problems-class-12-physics-electrostatic-potential-and-capacitance-14

Q 33.

In the circuit shown in figure initially key K1  
is closed and key K2 is open. Then K1 is opened and K2 is closed (order is important).
[Take Q’1 and Q’2 as charges on C1 and C2 and V1 and V2 as voltage respectively.]
Then, E
(a) charge on C, gets redistributed such that V1 = V2
(b) charge on C1 gets redistributed such that Q’1 = Q’2
(c) charge on C1 gets redistributed such that C1V1 + C2V2 = C1E
(d) charge on C1 gets redistributed such that Q’1 + Q’2=Q

ncert-exemplar-problems-class-12-physics-electrostatic-potential-and-capacitance-14

Q 34.

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?

ncert-exemplar-problems-class-12-physics-electrostatic-potential-and-capacitance-17

Q 35.

Find the equation of the equipotentials for an infinite cylinder of radius r0 carrying charge of linear density A.

Q 36.

Two charges q1 and q2 are placed at (0, 0, d) and (0, 0, -d) respectively. Find
the locus of points where the potential is zero.

Q 37.

You are given an air filled parallel plate capacitor C1. The space between its plates is now filled with slabs of dielectric constants Kx and K2 as shown in figure. Find the capacitance of the capacitor C2 if area of the plates is A and distance between the plates is d.
important-questions-for-class-12-physics-cbse-capactiance-t-22-20

Q 38.

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]

Q 39.

A hollow metal sphere of radius  5 cm is charged such that potential on its surface is 10 V. What is the potential at the centre of the sphere?           [All India 2011]

Q 40.

Can two equipotential surface  intersect each other? Justify your answer. [Delhi 2011 c]

Q 41.

important-questions-for-class-12-physics-cbse-electrostatic-potential-t-2-19

Q 42.

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]

Q 43.

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
ncert-exemplar-problems-class-12-physics-electrostatic-potential-and-capacitance-4

Q 44.

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) S1 is true but S2 is false
(b) Both S1 and S2 are false
(c) S1  is true, S2 is also true and 5, is the cause of S2
(d) S2  is true, S2 is also true but the statements are independent

Q 45.

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

Q 46.

Can the potential function have a maximum or minimum in free space?

Q 47.

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

Q 48.

In the circuit shown in figure, initially K1 is closed and K2 is open. What are the charges on each capacitors?
Then K1 was opened and K2 was closed (order is important), what will be the charge on each capacitor now? [C = 1 μF]
ncert-exemplar-problems-class-12-physics-electrostatic-potential-and-capacitance-28

Q 49.

Define the dielectric constant of a medium. What is its unit? [Delhi 2011c]

Q 50.

In the figure given below X, Y represent parallel plate capacitors having the same area of plates and the same distance of separation between them. What is the relation between the energies stored in the capacitors?
important-questions-for-class-12-physics-cbse-capactiance-t-22-11