Can the potential function have a maximum or minimum in free space?
No, the potential function does not have a maximum or minimum in free
space, it is because the absence of atmosphere around conductor prevents the phenomenon of electric discharge or potential leakage.
A parallel plate capacitor is charged by a battery. After sometime, the battery is disconnected and a dielectric slab with its thickness equal to the plate separation is inserted between the plates. How will
(i)the capacitances of the capacitor,
(ii)potential difference between the plates and
(iii)the energy stored in the capacitors be affected? Justify your answer in each case.[Delhi 2010]
Prove that a closed equipptential surface with no charge within itself must enclose an equipotential volume.
Two parallel plate capacitors of capacitances Cx and C2 such that Cx =2C2 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]
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]
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]
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?
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.
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.
Two parallel plate capacitors of capacitances Qand C2 such that q =C2 /2 are connected across a battery of V volts 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]
Find out the expression for the potential energy of a system of three charges q1, q2 and g3 located at q , r2 and r3 with respect to the common origin O. [Delhi 2010 c]
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.
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.
(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]
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?
(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]
Why there is no work done in moving a charge from one point to another on an equipotential surface? [Foreign 2012]
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
A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as ε= 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.
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]
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
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]
Name the physical quantity whose SI unit is J/C. Is it a scalar or a vector quantity? [All India 2010]
What is the electric potential due to an electric dipole at an equatorial point?[All India 2009]
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]
Define the terms (i)capacitance of a capacitor (ii)dielectric strength of a dielectric
(iii)When a dielectric is inserted between the plates of a charged parallel plate capacitor fully occupying the intervening region, how does the polarisation of the dielectric medium affect the net electric field? For a linear dielectric,show that the introduction of the dielectric increases its capacitance by a factor K which is a characteristic of the dielectric. [Delhi 2008 C]
Why electrostatic potential is constant throughout the volume of the conductor and has the same value as on its surface? [Delhi 2012]
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]
Can two equipotential surface intersect each other? Justify your answer. [Delhi 2011 c]
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]
What is the electric potential due to an electric dipole at an equatorial point?[All India 2009]
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]
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]
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
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.
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) 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.
Calculate potential on the axis of a disc of radius R due to a charge Q
uniformly distributed on its surface.
