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]
(i) Depict the equipotential surfaces for a system of two identical positive point charges placed a distance d apart.
(ii) Deduce the expression for the potential energy of a system of two point charges q1 and q2 brought from infinity to the points with positions and r2 respectively, in presence of external electric field E. [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]
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.
Why is the potential inside a hollow spherical charged conductor is constant and has the same value as on its surface?[Foreign 2012]
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 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.
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 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.
Why there is no work done in moving a charge from one point to another on an equipotential surface? [Foreign 2012]
(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.
What is the electric potential due to an electric dipole at an equatorial point?[All India 2009]
Name the physical quantity whose SI unit is J/C. Is it a scalar or a vector quantity? [All India 2010]
Define the term potential energy for charge q at a distance r in an external field. [All India 2009]
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]
For any charge configuration,equipotential surface through a point is a normal to the electric field. Justify. [Delhi 2014]
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]
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
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?
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]
A point charge Q is placed at point O as shown in the figure. Is the potential difference (VA – VB)
positive, negative or zero if Q is (i)positive (ii) negative
What is the electric potential due to an electric dipole at an equatorial point?[All India 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]
(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]
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
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
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
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 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.
Calculate the potential on the axis of a ring due to charge Q uniformly distributed along the ring of radius R.
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.
Calculate potential on the axis of a disc of radius R due to a charge Q
uniformly distributed on its surface.
