# Electrostatic Potential and Capacitance

### Question:

Two point charges of magnitude +q and -q are placed at (-d/2, 0, 0) and (d/2, 2, 0), respectively. Find the equation of the equipotential surface where the potential is zero.

Let the required plane lies at a distance x from the origin as shown in figure.

### 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.

(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 3.

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 4.

Find the charge on the capacitor as Shown in the circuit. [Foreign 2014]

#### Q 5.

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

#### Q 6.

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 7.

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]

#### Q 8.

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 9.

Find the charge on the capacitor as Shown in the circuit. [Foreign 2014]

#### Q 10.

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

#### Q 11.

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

#### Q 12.

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

#### Q 13.

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

#### Q 14.

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 15.

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

#### Q 16.

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 17.

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

#### Q 18.

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

#### Q 19.

A capacitor of 4 Î¼F is connected as shown in the circuit. The internal resistance of the battery is 0.5 â„¦. The amount of charge on the capacitor plates will be
(a) 0 (b) 4 Î¼C
(c) 16 Î¼C (d) 8 Î¼C

#### Q 20.

(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 21.

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

#### Q 22.

(i) Derive the expression for the  capacitance of a parallel plate capacitor having plate area A and plate separation d.
(ii) Two charged spherical conductors of radii and 1^ when connected by a conducting plate respectively. Find the ratio of their surface charge densities in terms of their radii. [Delhi 2014]

#### Q 23.

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 24.

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 25.

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 26.

Do free electrons travel to region of higher potential or lower potential?

#### Q 27.

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

#### Q 28.

If a conductor has a potential Vâ‰ 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 29.

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 U0  = 78 V. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.

#### Q 30.

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 Î¼F]

#### Q 31.

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.

#### Q 34.

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?

#### Q 35.

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 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.

Define dielectric strength of a dielectric. [Delhi 2008 C]

#### Q 38.

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?

#### Q 39.

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?

#### Q 40.

Distinguish between a dielectric and  a conductor.  [Delhi 2012]

#### Q 41.

Find the charge on the capacitor as Shown in the circuit. [Foreign 2014]

#### Q 42.

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

#### Q 43.

Equipotential surfaces
(a) are closer in regions of large electric fields compared to regions of lower electric fields
(b) will be more crowded near sharp edges of a conductor
(c) will be more crowded near regions of large charge densities
(d) will always be equally spaced

#### Q 44.

What is the work done in moving a  test charge q through a distance of 1 cm along the equatorial axis of an electric dipole?   [All India 2009]

#### Q 45.

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

#### Q 46.

Consider two conducting spheres of radii R1 and R2 with R1 > R2. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.

#### Q 47.

(i) A parallel plate capacitor is  charged by a battery to a potential. The battery is disconnected and a dielectric slab is inserted to completely fill the space between the plates.
How will
(a)its capacitance
(b)electric field between the plates and
(c)energy stored in the capacitor be affected? Justify your answer giving necessary mathematical expressions for each case.
(ii) (a) Draw the electric field lines due to a conducting sphere.
(b) Draw the electric field lines due to a dipole.

#### Q 48.

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

#### Q 50.

The potential due to a dipole at any point on its axial line is zero.  [All India 2009 C]