## JEE Main Previous Year Papers Questions With Solutions Physics Electrostatics

Multiple Choice with ONE correct answer
1.A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 volt. The potential at the centre of the sphere is  [1983- Imark]
a) zero b) 10 volt
c)same as at a point 5 cm away from the surface
d)same as at a point 25 cm away from the surface

Ans.(b) Electric potential at any point inside a hollow metal sphere is constant. The potential at the surface is 10 volt. The potential at the centre will also be 10

2.Two point charges +q and -q are held fixed at  (-d,0) and (d,0) respectively of a x-y coordinate system. Then             [1995-2 marks]
a)The electric field E at all points on x-axis has the same direction
b)Electric field at all points on y-axis is along x-axis
c)Work has to be done in bringing a test charge from infinity to the origin
d)The dipole moment is 2qd along the x-axis

Ans.(b) (a) E on x-axis E will not have same direction along entire x-axis. Option (a) is incorrect.

For – d < x < d, the field is along +x-axis For all other points, E is along negative x-axis
b)Electric field at P, a point on y-axis is parallel to x-axis. It is not along x-axis itself. It is nearest to correct answer.
c)Electric potential at origin is zero  No work has to be done in bringing a test charge from infinity to the origin. Option (c) is incorrect
d)The dipole moment is directed from -q charge to +q charge, along negative direction, of x-axis.
.•. Dipole moment = -2qd along x-axis.
The option is incorrect.Hence option (b) is nearest to correct answer.

3.A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V. Another capacitor of capacitance 2C is similarly charged to a potential difference 2V. The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is  [1995-2 marks]

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4.An electron of mass me, initially at rest, moves through a certain distance in a uniform electric field in time tr A proton of mass mp) also initially at rest, takes time t2 to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio of t, /1, is nearly equal to[1997-1 mark]
a) 1                                 b) (mp/me)1/2
c) (me/mp)1/2                 d) 1836

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Ans.(d) Resistor (R) and capacitor (C) are connected in  parallel. They are connected across a 1.5 volt source of negligible resistance.Since the capacitor is directly connected to voltage source and there is no resistance in the path,

7.Two identical metal plates are given positive charges Q1 and Q2 (<Q1) respectively. If they are now brought close together to form a parallel plate capacitor with capacitance C, the potential difference between them is [1999-2 marks]
a) (Q1+Q2)/(2C)          b) (Q1+Q2)/C
c)(Q1-Q2)/C                 d) (Q1-Q2)/(2C)

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8.For the circuit shown in figure, which of the following statement is true ?  [ JEE ’99, 2 ]
a)with S1 closed, V1 = 15 V, V2 = 20 V
b)with S3 closed, V1 = V2 = 25 V
c)with S1 & S2 closed, V1 = V2 = 0
d)with S1 & S3 closed, V1 = 30 V, V2 = 20 V

Ans.(d) No change of any potential across any capacitor  will occur unless the two capacitors Cj and C2 are either connected in series or in parallel.Charges would be maintained as they are unless Sj, S2 and S3, all are closed.This condition is given in none of the options. Hence the potentials of C1 and C2 will be maintained as V1 = 30 volt and V2 = 20 volt, with S, and S3 closed.

9.Three charges Q, -i-q and -t-q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero

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10.A parallel plate capacitor of area A, Plate separation d and capacitance C is filled with three different dielectric materials having dielectric constant Kp K2 and K3 as shown in the figure. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric  constant K is given by

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11.Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in  [JEE 2001-1 mark]

Ans.(c) Electric lines of force do not end at positive charge as shown in (a). The option is therefore incorrect. Electric lines of force never form a closed loop. Options (b) and (d) are incorrect.Option (c) represents correct answer. Mutual repulsion between similar charges is depicted in figure.

12.Consider the situation shown in the figure. The capacitor A has a charge q on it whereas B is uncharged. The charge appearing on the capacitor B a long time after the switch is closed is  [2001-1 mark]

Ans.(a) Due to attraction of positive charge, the negative charge is bound and so it will not flow to capacitor B through the switch S.Option (a) represents the correct answer.

13.A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be the point on  the x-axis at x=+l cm and C be the point on the y-axis at Y=+l cm. Then the potentials at the points A,B and C satisfy.  [2001-1 mark
a)VA<VB     b)VA>VB   c) VA<Vc    d)VA>Vc

Ans.(b) Potential decreases as we move along the direction of electric field. The field E is uniform and runs patallel to x-axis.Any line perpendicular to x-axis is an equipotential line.

14.Two equal point charges are fixed at x = -a and  x = +a on the axis. Another point charge Q is placed at the origin. The change in the electrical potential energy of Q, when it is displaced by a small distance x along the x-axis, is approximately proportional to     [JEE 2002-1 mark]
a)x     b) x2       c) x3       d) 1/x

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15.Two identical capacitors, have the same capaci ­tance C. One of them is charged to potential Vj and the other V2. The negative ends of the capaci ­tors are  connected together. When the positive ends are also connected, the decrease in energy of the combined system is[JEE 2002 (Scr), 3]

Ans.(c) When two capacitors joined together by connecting positive plate to positive plate and negative plate to negative plate, then the loss of  mechanical energy or heat produced or work done to drive the change is given by

16.A metalic shell has a point charge q kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of force?  [JEE’2003 (scr)]

Ans.(c) Field lines do not enter the metallic portion of the shell as field is zero inside the metal. Hence options (a) and (d) are incorrect.The field lines are normal to metal surface.Hence option (b) is incorrect.Both the conditions are satisfied in option (c), Hence (c) represents the correct answer.

17.Six charges of equal magnitude , 3 negative are to be placed on PQRSTU comers of a regular hexagon, such that field at the centre is double that of what it would have been if only one +ve charge is placed at R.  [2004-1 mark]

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(c) According to option (c), the electric fields at O  due to
i)P and S nullify each other
ii)Q and T nullify each other
iii)R and U add up to 2E
Hence option (c) represents the answer.

18.A Gaussian surface in the figure is shown by dotted  line. The electric field on the surface will be  [2004-1 mark]

Ans.(d) At any point over the spherical Gaussian msurface, net electric field is the vector sum of electric fields due to all the three charges +qp -q1  and q2.

19.Three infinitely long charge sheets are placed as shown in figure. The electric field at point P is  [2005-1 mark]

Ans.(c) All the three charge sheets will produce electric  field at P. The field will be along negative Z-axis.Hence

20.Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then. [2007-3 marks]
a)negative and distributed uniformly over the surface of the spher
b)negative and appears only at the point on the sphere closest to the point charge
c)negative and distributed non-uniformly over the entire surface of the sphere
d)zero

Ans.  (d) When a positive point charge is placed outside a conducting sphere, a rearrangement of charge take place on the surface.But the total charge on the sphere is zero as no  charge has left or entered the sphere.

21.A long, hollow conducting cylinder is kept  coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.   [2007-3 marks]
a)A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
b)A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.
c)No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders.
d)No potential difference appears between the two cylinders when  same charge density is given to both the cylinders.

Ans.(a) When a charge density is given to the inner  cylinder, the potential developed at its surface is
different from that on the outer cylinder. This is  because the potential decreases with distance for a
charged conducting cylinder when the point of  consideration is outside the cylinder.
But when a charge density is given to the outer  cylinder, it will change its potential by the same amount as that of the inner cylinder. Therefore no potential difference will be produced between the cylinders in this case.

22.A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is [2007-3 marks]

a)zero everywhere
b)non-zero and uniform
c)non-uniform
d)zero only at its center.

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Ans.It can be seen that potential at both points A and B  are zero. When the charge is moved from A to B, work done by the electric field on the charge will be zero.

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25.A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K=2. The level of liquid is d/3 initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is  [2008]

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27.Under the influence of the Coulomb field of charge +Q, a charge -q is moving around it in an elliptical orbit. Find out the correct statement(s). (2009)
a)The angular momentum of the charge -q is constant
b)The linear momentum of the charge -q is constant
c)The angular velocity of the charge -q is constant
d)The linear speed of the charge -q is constant

Ans.(a) The angular momentum of the charge -q is constant

28.A disk of radius a/4 having a uniformly distributed charge 6C is placed in the x-y plane with its centre at (-a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x = 5a/4. Two point charges -7C and 3C are placed at (a/4, -a/4, 0) and (-3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces x = ±a/2, y = +a/2, z = +a/2. The electric flux through this cubical surface is(2009)

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29.Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q1 Q2, Q3, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then the ratio of the charges given to the shells, Q1 : Q2: Q3, is (2009)
a)1 : 2 : 3   b) 1 : 3 : 5   c) 1 : 4 : 9   d) 1 : 8 : 18

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Multiple Choice with ONE or    More Than ONE correct answers
32.Two equal negative charge -q are fixed at points (0, -a) and (0, a) on y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge Q will. [1984-2 marks]
a)execute simple harmonic motion about the origin
b)move to the origin remain at rest
c)move to infinity
d)execute oscillatory but not simple harmonic motion.

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33.A parallel plate air capacitor is connected to a battery. The quantites charge, voltage, electric field and energy associated with this capacitor are given by Q0,V0,E0 and U0 A dielectric slab is now introduced to fill the space between the plates with battery still in connection. The corresponding quantities now given by Q, V< E and U are related to the previous one as [1985-2 marks]
a)Q >Q0     b) V > V0     c) E >E0     d)U>U0

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34.A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to  [1987-2 marks]

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35.A parallel plate capacitor is charged and the  charging battery is then disconnected. If the plates of the capacitor are moved farther apart by means of insulating handles  [1987-2 marks]
a)the charge on the capacitor increases
b)the voltage across the plates increases
c)the capacitance increases
d)the electrostatic energy stored in the capacitor increases.

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36.A solid conducting sphere having a charge Q is  surrounded by an uncharged concentric conduct ­ing hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of -3Q, the new potential difference between the same two surfaces is           [1989-2 marks]
a) V     b) 2V      c) 4V     d) -2V

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38.A parallel plate capacitor of plate area A and plate separation d is charged to potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q,E and W denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted), and the workdone on the system, in question, in the  process of inserting the slab, then [1991-2 marks]

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39.Two identical thin rings, each of radius R metre, are coaxially placed at a distance R metre apart. If Q1 coulomb and Q2 coulomb, are respectively the charges uniformly spread on the two rings, the work done in moving charge q from the centre of one ring to that of the other is [1992-2 marks]

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40.The magnitude of electric field E in the annular region of a charged cylindrical capacitor
a)Is same throughout [IIT’96, 2]
b)Is- higher near the outer cylinder than near the inner cylinder
c)Varies as (1/r), where r is the distance from axis
d)Varies as (1/r2), where r is the distance from axis

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41.A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s)

Ans.(d) The lines of force never enter a metallic sphere because intensity is zero inside a conductor/metal. Hence options (b) and (c) are incorrect.The lines of force are at normal to the surface. Hence option (a) is incorrect.Option (d) represents the correct answer.

42.A dielectric slab of thickness d is inserted in a parallel plate capacitor whose negative plate is at x=0 and positive plate is at x=3d. The slab is equidistant from the plates. The capacitor is given some charge. As one goes from 0 to 3d,  [1998-2 marks]
a)the magnitude of the electric field remains the same
b)the direction of the electric field remains the same
c)the electric potential increases continuously
d)the electric potential increases at first, then decreases and again increases.

Ans.b)The direction of electric field remains the same. Option (b) is therefore correct.
c)Electric field lines always flow from higher potential to lower potential. The electric potential V, therefore, increases continuously as one goes from x = 0 to x = 3d. OA || BC  Slope of (OA) > slope of AB Option (c) is correct.
d)The option is incorrect. Refer to figure (iii)

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Ans.(c), (d) Points A and B lie on the ellipsoidal cavity  carved within a perfect conductor. Since the

potential of all points which lie on the conductor,is same,the potentials at A and B are same.
Potential at A=Potential at B  Option (c) is correct.According to Gauss theorem,Hence option (d) is correct.Options (a) and (b) are incorrect as the cavity is  ellipsoidal. It may, however, be noted that options  (a) and (b) hold good in case of a spherical caivty.

47.spherical symmetric charge system is centred at origin. Given, electric potential [2006-5 marks]

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48.A few electric field for a system of two charges Q, and Q2 fixed at two different points on the x-axis are shown in the figure. These lines susggest that

Ans.(a), (d) Number of lines of force is directly pro-  portional to the magnitude of the charge  so |Qi|>|Q2|
At null point where E = 0, there will be no lines of force of only the given two charges are consid ­ered, there is a chance of getting E = 0 to the right of Q2 (Null point will be closer to the charge hav ­ing small magnitude)

49.A spherical metal shell A of radius RA and a solid metal sphere B of radius RB (<RA) are kept far apart and each is given charge â€˜+Q’. Now they are con ­nected by a thin metal wire. (2011)

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50.Which of the following statement(s) is / are correct
a)If the electric field due to a point charge varies  as r2 5 instead of r2, then the Gauss law will still be valid       (2011)
b)the gauss law can be used to calculate the field distribution around an electric
c)If the electric field between two point charges is zero some where, then the sign of the two charges is the same
d)the work done by the external force in moving a unit positive charge from point A at potential VA to potential VB is (VB – VA)

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Assertion – Reasoning type
Instructions : The following question contains statement-I (assertion) and statement -2 (reason) of these statements, mark correct choice if
a)Statement-1 and 2 are true and statement-2 is a correct explanation for statement-1
b)Statement-1 and2 are true and statement-2 is not a correct explanation for statement-1
c)Statement-1 is true, statement-2 is flase d) Statement-1 is false, statement-2 is true.

51.Statement -1 : For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
Statement -2 : The electrical potential of a sphere of radius R with charge Q uniformly distributed on the

Ans.(b) Statement -1 is true, you all are familiar with this convention.Statement – 2 is true. You all know this, recall the shell theorem.But statement -2 is not the correct explanation of statement – 1.

Comprehension based question
The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density p(r) [charge per unit volume] is dependent only on the radial distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.

52.The electric field at r = R is
a) independent of a b) directly proportional to a c) directly proportional to a2 d) inversely proportional to a
Ans.(a) Electric field at a distance R from the centre of the nucleus es,

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54.The electric field within the nucleus is generally observed to be linearly dependent on r. This implies
a)a=0  b)R/2   c)a=R   d)2R/3
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Matching type
Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column – II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M (Potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let B be the magnetic field at M and p be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current. [2009]

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56.A rigid insulated wire frame in the form of a right angled triangle ABC, is set in a vertical plane as shown in fig. Two beads of equal masses m each and carrying charges qj and q7 are connected by a cord of length / and can slide without friction on the wires.Considering the case when the beads are stationary determine   [1978]
Ans.(a) Consider first the equilibrium of bead at P, having charge qr Different forces acting on it are shown in the figure. If the charges qj and q2 are similar in nature, then electric force F will be repulsive and is given by

57.A charged particle is free to move in an electric field. Will it always move along an electric line of force? [1979]
Ans.It moves along the line of force only if it is straight.

58.A charge Q is distributed over two concentric hollow spheres of radii r and R (>r) such that the surface densities are equal. Find the potential at the common centre.  [1981-3 marks]
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59.The figure shows two identical parallel plate capacitors connected to a battery with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant (or relative permittivity) 3. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.

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Ans.The moving charge -q has potential and kinetic energies while at C and at D. The sum of the two energies at C and D remains constant.

61.Three point charges q, 2q and 8q are to be placed on a 9 cm long straight line. Find the positions where the charges should be placed such that the potential energy of this system is minimum. In this situation, what is the electric field at the position of the charge q due to the other two charges?  [1987-7 marks]
Ans.The potential energy will be minimum when the two bigger charges are located at maximum dis ­tance in the system. Let x cm = x x 10-2m, be the distance between 2q and q.

62.Three particles, each of mass lg and carrying a  charge q, are suspended from a common point by insulated massless strings, each 100 cm long. If the particles are in equilibrium and are located at the comers of an equilateral triangle of side length 3cm, calculate the charge q on each particle. (Take g = 10m/s2)  [1988-5 marks]
Ans.Each particle of mass m and charge q is suspended by a 100 cm long string, m=l gram. They are located at corners of an equilateral triangle of sidelength 3 cm. Three forces act on each particle.

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64.Two fixed charges -2Q and Q are located at the points with coordinates (-3a, 0) and (+3a, 0) respectively in the x-y plane. [1991-4+2+2 marks]
a)Show that all points in the x-y plane, where the electric potential due to the two charges is zero, lie on a circle. Find its radius and the location of its centre.
b)Give the expression V(x) at a general point on the x-axis and sketch the function V(x) on the whole x-axis
c)If a particle of charge +q starts from rest at the the centre of the circle, show by a short quantitative argument that the particle eventually crosses the circle. Find its speed when it does so.

Ans.Charge (-2Q) is located at (-3a, 0) in x-y  plane  Charge (Q) is located at (+3a, 0) in x-y plane, a) Locus of zero potential:Let P be a general point, denoted by (x,y), wher potential due to the two charges is zero.

65.a) A charge of Q coulomb is uniformly distributed over a spherical volume of radius R metre. Obtain an expression for the energy of the system.
b)What will be the corresponding expression for the energy needed to completely disassemble the planet earth against the gravitational pull amongest its constituent particles?
Assume the earth to be a sphere of uniform mass density. Calculate this energy, given the product of the mass and the radius of the earth to be 2.5 x l031kg.m.
c)If the same charge of Q coulomb as in part a) above is given to a spherical conductor of the same radius R, what will be energy of the system?  [1992-10 marks]

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66.Two parallel plate capacitors A & B have the same separation d = 8.85 x 10-4 m between the plates. The plate area of A & B are 0.04 m2 & 0.02 m2 respectively. A slab of di-electric constant (relative permittivity) K=9 has dimensions such that it can exactly fill the capacitor between the plates of [1999-7]
i)the di-electric slab is placed inside A as shown in the figure (a) A is then charged to a potential difference of 110 volt. Calculate the capacitance of A and the energy stored in it.
ii)the battery is disconnected & then the di-electric slab is moved from A . Find the work done by the external agency in removing the slab from A
iii)the same di-electric slab is now placed inside B, filling it completely. The two capacitors A & B are then connected as shown in figure (c). Calculate the energy stored in the system.

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68.Two square metal plates of 1 m side are kept 01 m apart, like a parallel plate capacitor, in air in such a way that one of their edges is perpendicular, to an oil surface in a tank filled with an insulating oil. The plates are connected to a battery of e.m.f. 500 volt . The plates are then lowered vertically into the oil at a speed of 0.001 m/s. Calculate the current drawn from the battery during the process, [di-electric constant of oil = 11, E0 = 8.85 x 10-12 C2/N1 m1] [JEE ’94, 6]
Ans.As here battery remains attached to the circuit V=constant. Now as due to lowering of plates in the oil, capacity will increase gradually and as q=CV the charge on capacitor will increase. This gradual increase in q results in current drawn from the battery.If at any instant, y length of plate is dipped in oil, the system will be equivalent to two capacitors in parallel, one with air and the other with oil as dielectric so that

69.The capacitance of a parallel plate capcitor with plate area ‘A’ & separation d is C. The space between the plates is filled with two wedges of di-electric constants. Kt & K2 Find the capacitance of the resulting capacitor. [JEE’96,2]
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70.Two isolated metallic solid spheres of radii R and 2R are charged such that both of these have same charge density a . The spheres are located far away from each other, and connected by a thin conducting wire. Find the new charge density on the bigger sphere.   [1996-3 marks]
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71.Two capacitors A and B with capacities 3 mF and 2 mF are charged to a potential difference of 100 V and 180 V respectively. The plates of the capacitors are connected as shown in the figure with one wire from each capacitor free. The upper plate of A is positive and that of B is negative. An uncharged 2 mF capacitor C with lead wires falls on the free ends to complete the circuit. Calculate  [ JEE ’97 -5 marks]
i)the final charge on the three capacitors and
ii)The amount of electrostatic energy stored in the system before and after the completion of the circuit.

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72.A conducting sphere S1 of radius r is attached to an insulating handle . Another conducting sphere S2 of radius R is mounted on an insulating stand. S2 is initially uncharged . S1 is given a charge Q, brought into contact with S2 & removed, S1 is recharged such that the charge on it is again Q & it is again brought into contact with S2 & removed. This procedure is repeated n times.[1998-8 marks]
a)Find the electrostatic energy of S2 after n such contacts with S1
b)What is the limiting value of this energy as n->infinity?

Ans.When a conducting sphere S, is brought in con ­tact with another conducting sphere S2, a transfer of charge occurs from higher potential to lower  potential till the two spheres attain equal potential. Let S1 contain charge Q before contact with S2. On contact, let a charge q shift from S1 to S2

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