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) 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.
Prove that a closed equipptential surface with no charge within itself must enclose an equipotential volume.
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]
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 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.
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]
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]
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]
For any charge configuration,equipotential surface through a point is a normal to the electric field. Justify. [Delhi 2014]
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]
Calculate potential on the axis of a disc of radius R due to a charge Q
uniformly distributed on its surface.
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]
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?
Why there is no work done in moving a charge from one point to another on an equipotential surface? [Foreign 2012]
Name the physical quantity whose SI unit is J/C. Is it a scalar or a vector quantity? [All India 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, Cl and C2 with their capacitances in the ratio 1 : 2, so that the energy stored in the two cases becomes the same[Foreign 2010]
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]
What is the electric potential due to an electric dipole at an equatorial point?[All India 2009]
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 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 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.
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.
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]
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]
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
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.
(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]
(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 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
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
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 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]
(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) Two points charges qx and q2 initially at infinity, are brought one by one to points Px and P2 specified by position vectors rt and r2 relative to same origin. What is the potential energy of this charge configuration? Define an equipotential surface.
(ii) Draw schematically the equipotential surface corresponding to a field that uniformly increases in magnitude but remains constant in direction. [Delhi 2008]
