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
(c)
Key concept: For a given charge distribution, locus of all points or regions for which the electric potential has a constant value are called equipotential regions. Such equipotential can be surfaces, volumes or lines. Regarding equipotential surface the following points should be kept in mind:
• The density of the equipotential lines gives an idea about the magnitude of electric field. Higher the density, larger the field strength.
• The direction of electric field is perpendicular to the equipotential surfaces or lines.
• The equipotential surfaces produced by a point charge or a spherically charge distribution are a family of concentric spheres.
• For a uniform electric field, the equipotential surfaces are a family of plane perpendicular to the field lines.
• A metallic surface ofany shape is an equipotential surface.
• Equipotential surfaces can never cross each other.
• The work done in moving a charge along an equipotential surface is always zero.
As the direction of electric field is always perpendicular to one equipotential surface maintained at high electrostatic potential than other equipotential surface maintained at low electrostatic potential. Hence direction of electric field is from B to A in all three cases.
The positively charged particle experiences electrostatic force along the direction of electric field, hence moves in the direction opposite to electric field. Thus, the work done by the electric field on the charge will be negative. We know
Here initial and final potentials are same in all three cases and same charge is moved, so work done is same in all three cases.
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]
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 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 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 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.
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 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.
(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.
Calculate the potential on the axis of a ring due to charge Q uniformly distributed along the ring of radius R.
Calculate potential on the axis of a disc of radius R due to a charge Q
uniformly distributed on its surface.
(i)Write two characteristics of equipotential surfaces.
(ii) Draw the equipotential surfaces due to an electric dipole. [All India 2009 C]
A dipole with its charge -q and +q located at the points (0, – b,0) and (0,+ 5,0) is present in a uniform electric field E. The equipotential surfaces of this field are planes parallel to the Y Z-plane.
(i)What is the direction of the electric field E?
(ii)How much torque would the dipole experience in this field?[Delhi 2010 C]
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]
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]
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]
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
Find the equation of the equipotentials for an infinite cylinder of radius r0 carrying charge of linear density A.
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]
Determine the potential difference across the plates of the capacitor Cx of the network shown in the figure, (assume, E2 >E1 ) [All India 2013]
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.
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]
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
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
(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]
The potential due to a dipole at any point on its axial line is zero. [All India 2009 C]
What is the electric potential due to an electric dipole at an equatorial point?[All India 2009]
Prove that a closed equipptential surface with no charge within itself must enclose an equipotential volume.
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?
