Define the term potential energy for charge q at a distance r in an external field. [All India 2009]
The electric potential energy at any point lying at a distance r from the source charge q is equal to the amount of work done in moving unit positive test charge from infinity to that point without any acceleration against of electrostatic force.
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.
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.
Why is the potential inside a hollow spherical charged conductor is constant and has the same value as on its surface?[Foreign 2012]
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 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]
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.
(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.
(i)Write two characteristics of equipotential surfaces.
(ii) Draw the equipotential surfaces due to an electric dipole. [All India 2009 C]
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]
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.
Why there is no work done in moving a charge from one point to another on an equipotential surface? [Foreign 2012]
Find the equation of the equipotentials for an infinite cylinder of radius r0 carrying charge of linear density A.
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]
Determine the potential difference across the plates of the capacitor Cx of the network shown in the figure, (assume, E2 >E1 ) [All India 2013]
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]
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
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]
Name the physical quantity whose SI unit is J/C. Is it a scalar or a vector quantity? [All India 2010]
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]
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 charges of 5 nC and – 2 nC are placed at points (5 cm, 0, 0) and (23 cm, 0, 0) in the region of space, where there is no other external field. Calculate the electrostatic potential energy of this charge system.[Delhi 2008 C]
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
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
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
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
