## JEE Main Physics Electrostatics Previous Year Questions with Solutions

For JEE Main other Engineering Entrance Exam Preparation,Â **JEE Main Physics Electrostatics**Â Previous Year Questions with Solutions is given below.

**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 isÂ [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 atÂ (-d,0) and (d,0) respectively of a x-y coordinate system. ThenÂ Â Â Â Â Â [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 zeroÂ 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.

.â€¢. 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 isÂ [1995-2 marks]**

**Ans.**

**4.An electron of mass m _{e}, initially at rest, moves through a certain distance in a uniform electric field in time t_{r} A proton of mass m_{p)} also initially at rest, takes time t_{2} 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 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â b) (m_{p}/m_{e})^{1/2}

c) (m_{e}/m_{p})^{1/2}Â Â Â Â Â Â Â Â d) 1836

**Ans.**

**Ans.**

**Ans.**(d) Resistor (R) and capacitor (C) are connected inÂ 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 Q _{2} (<Q_{1}) 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+Q**

c)(Q1-Q

_{2})/(2C) Â Â Â Â Â b) (Q_{1}+Q_{2})/Cc)(Q1-Q

_{2})/C Â Â Â Â Â Â Â Â d) (Q_{1}-Q_{2})/(2C)**Ans.**

**8.For the circuit shown in figure, which of the following statement is true ? Â [ JEE ’99, 2 ]
a)with S1 closed, V1 = 15 V, V _{2} = 20 V
b)with S_{3} closed, V_{1} = V_{2} = 25 V
c)with S1 & S_{2} closed, V_{1} = V_{2} = 0
d)with S1 & S_{3} closed, V1 = 30 V, V_{2} = 20 V**

**Ans.**(d) No change of any potential across any capacitorÂ will occur unless the two capacitors Cj and C

_{2}are either connected in series or in parallel.Charges would be maintained as they are unless Sj, S

_{2}and S

_{3}, all are closed.This condition is given in none of the options. Hence the potentials of C1 and C

_{2}will be maintained as V1 = 30 volt and V

_{2}= 20 volt, with S, and S

_{3 }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**

**Ans.**

**10.A parallel plate capacitor of area A, Plate separation d and capacitance C is filled with three different dielectric materials having dielectric constant K _{p }K_{2} and K_{3} 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 dielectricÂ constant K is given by**

**Ans.**

**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 inÂ [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 isÂ [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 onÂ 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.Â [2001-1 mark
a)V _{A}<V_{B}Â Â b)V_{A}>V_{B Â c) }V_{A}<V_{c}Â Â d)V_{A}>V_{c}**

**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 andÂ 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 toÂ Â [JEE 2002-1 mark]
a)x Â Â b) x ^{2 Â Â Â } c) x^{3}Â Â Â d) 1/x**

**Ans.**

**15.Two identical capacitors, have the same capaciÂtance C. One of them is charged to potential Vj and the other V _{2}. The negative ends of the capaciÂtors are Â 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 ofÂ 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?Â [JEEâ€™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.Â [2004-1 mark]**

**Ans.**

(c) According to option (c), the electric fields at OÂ 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 dottedÂ line. The electric field on the surface will beÂ [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 +q_{p} -q1Â and q_{2}.

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

**Ans.**(c) All the three charge sheets will produce electricÂ 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.**Â (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 noÂ charge has left or entered the sphere.

**21.A long, hollow conducting cylinder is keptÂ coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.Â [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 whenÂ same charge density is given to both the cylinders.**

**Ans.**(a) When a charge density is given to the innerÂ cylinder, the potential developed at its surface is

different from that on the outer cylinder. This isÂ because the potential decreases with distance for a

charged conducting cylinder when the point ofÂ consideration is outside the cylinder.

But when a charge density is given to the outerÂ 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.**

**Ans.**

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

**Ans.**

**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 isÂ [2008]**

**Ans
**

**Ans.**

**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 = Â±a/2, y = +a/2, z = +a/2. The electric flux through this cubical surface is(2009)**

**Ans.**

**29.Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q _{1} Q_{2}, Q_{3}, 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, Q_{1} : Q_{2}: Q_{3}, is (2009)**

a)1 : 2 : 3 Â b) 1 : 3 : 5 Â c) 1 : 4 : 9 Â d) 1 : 8 : 18

**Ans.**

**Ans.**

**Ans.**

**Â Multiple Choice with ONE orÂ Â 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.**

**Ans.**

**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 Q _{0},V_{0},E_{0} and U_{0} 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 >Q_{0 Â Â } b) V > V_{0}Â Â c) E >E_{0}Â Â d)U>U_{0}

**Ans.**

**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 toÂ [1987-2 marks]**

**Ans.**

**35.A parallel plate capacitor is charged and theÂ charging battery is then disconnected. If the plates of the capacitor are moved farther apart by means of insulating handles Â [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.**

**Ans.**

**36.A solid conducting sphere having a charge Q isÂ surrounded by an uncharged concentric conductÂing 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 isÂ Â Â Â Â [1989-2 marks]
a) V Â Â b) 2V Â Â Â c) 4V Â Â d) -2V**

**Ans.**

**Ans.**

**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 Â process of inserting the slab, then [1991-2 marks]**

**Ans.**

**39.Two identical thin rings, each of radius R metre, are coaxially placed at a distance R metre apart. If Q1 coulomb and Q _{2} 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]**

**Ans.**

**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/r**

^{2}), where r is the distance from axis

**Ans.**

**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,Â [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 || BCÂ Slope of (OA) > slope of AB Option (c) is correct.

d)The option is incorrect. Refer to figure (iii)

**Ans.**

**Ans.**

**Ans.**

**Ans.**(c), (d) Points A and B lie on the ellipsoidal cavityÂ 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 BÂ Option (c) is correct.According to Gauss theorem,Hence option (d) is correct.Options (a) and (b) are incorrect as the cavity isÂ ellipsoidal. It may, however, be noted that optionsÂ (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]**

**Ans.**

**48.A few electric field for a system of two charges Q, and Q _{2} 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-Â portional to the magnitude of the chargeÂ so |Qi|>|Q

_{2}|

At null point where E = 0, there will be no lines of force of only the given two charges are considÂered, there is a chance of getting E = 0 to the right of Q

_{2}(Null point will be closer to the charge havÂing small magnitude)

**49.A spherical metal shell A of radius R _{A} and a solid metal sphere B of radius R_{B} (<R_{A}) are kept far apart and each is given charge â€˜+Qâ€™. Now they are conÂnected by a thin metal wire. (2011)**

**Ans.**

**50.Which of the following statement(s) is / are correct
a)If the electric field due to a point charge variesÂ as r ^{2 5} instead of r^{2}, then the Gauss law will still be validÂ Â Â (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 V_{A }to potential V_{B} is (V_{B} – V_{A})**

**Ans.**

**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**

**Read the passage given below and answer the questions that follow**

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 a ^{2} d) inversely proportional to a**

**Ans.**(a) Electric field at a distance R from the centre of the nucleus es,

**Ans.**

**54.The electric field within the nucleus is generally observed to be linearly dependent on r. This implies**

**a)a=0 Â b)R/2 Â c)a=R Â d)2R/3**

**Ans.**

**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]

**Ans.**

**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 q _{7} are connected by a cord of length / and can slide without friction on the wires.Considering the case when the beads are stationary determine Â [1978]**

**Ans.**(a) Consider first the equilibrium of bead at P, having charge q

_{r}Different forces acting on it are shown in the figure. If the charges qj and q

_{2}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. Â [1981-3 marks]**

**Ans.**

**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.**

**Ans.**

**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?Â [1987-7 marks]**

**Ans.**The potential energy will be minimum when the two bigger charges are located at maximum disÂtance in the system. Let x cm = x x 10-^{2}m, be the distance between 2q and q.

**62.Three particles, each of mass lg and carrying aÂ 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/s ^{2}) Â [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.

**Ans.**

**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-yÂ planeÂ 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 l0**

^{31}kg.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?Â [1992-10 marks]

**Ans.**

**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 m^{2} & 0.02 m^{2 }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.

**Ans.**

**Ans.**

**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, E _{0} = 8.85 x 10-^{12} C^{2}/N^{1} m^{1}] [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. K _{t} & K_{2} Find the capacitance of the resulting capacitor. [JEE’96,2]**

**Ans.**

**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. Â [1996-3 marks]**

**Ans.**

**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. CalculateÂ [ 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.**

**Ans.**

**72.A conducting sphere S1 of radius r is attached to an insulating handle . Another conducting sphere S _{2} of radius R is mounted on an insulating stand. S_{2} is initially uncharged . S1 is given a charge Q, brought into contact with S_{2} & removed, S1 is recharged such that the charge on it is again Q & it is again brought into contact with S_{2} & removed. This procedure is repeated n times.[1998-8 marks]**

a)Find the electrostatic energy of S_{2} after n such contacts with S_{1}

b)What is the limiting value of this energy as n->infinity?

**Ans.**When a conducting sphere S, is brought in conÂtact with another conducting sphere S

_{2}, a transfer of charge occurs from higher potential to lowerÂ potential till the two spheres attain equal potential. Let S1 contain charge Q before contact with S

_{2}. On contact, let a charge q shift from S1 to S

_{2}

**Ans.**

**Ans.**Let the particle be, at some instant, at a point P distant x from the origin. Of the four charges placed along y-axis, the like charges repel each other while the unlike charges attract each other. At some value of x, the attractive and repulsive forces balÂance each other. Therefore the attractive forces will move the charge towards origin.

**75.Charges +q and -q are located at the comers of a cube of side a as shown in the figure. Find the work done to separate the charges to infinite distance. Â [JEE 2003-2 marks]**

**Ans.**

**Ans.**(a) The free dipole, far away from the origin, travels towards origin, where a charge (+Q) is fixed. There will be a decrease in the electrostatic potential energy of the dipole. This will be equal to kinetic energy of the dipole. When the dipole is at a distance d from origin,

**Ans.**

**78.A conducting liquid bubble of radius a and thickness t (t << a) is charged to potential V. If the bubble collapses to a droplet, find the potential on the droplet. Â Â [2005-2 marks]
**

**Ans.**A liquid-bubble contains air inside and liquid in the outside surface. When the bubble collapses into a droplet, the volume of liquid remains same in the transformation.

**Ans.**

**Ans.**

**True / False type**

**81.The work done in carrying a point charge from one point to another in an electrostatic field depends on the path along which the point charge is carried. Â [1981-2 marks]**

**Ans.**Â False.Â Electrostatic force is conservative in nature. Work done in carrying a charge between two points does not depend upon path’ along which the charge is carried.The statement is false.

**82.Two identical metallic spheres of exactly equal masses are taken. One is given a positive charge Q coulomb and the other an equal
Ans.**True.The metallic sphere which acquires positive charges loses electrons and so it loses mass. The metallic sphere which gains negative chage gains electrons and so it gains mass. Their masses on charging are evidently different.The statement is true.

**83.A small metal ball is suspended in a uniform electric field with the help of an insulated thread. If high energy X-ray beam falls on the ball, the ball will be deflected in the direction of the field.[1983-2 marks]**

**Ans.**True.When a high energy X-ray beam falls on a metal ball, it ejects electrons from the ball. The ball therefore becomes positively charged and gets deflected in the direction of electric field.The statement is true.

**84.Two protons A and B are placed in between the two plates of a parallel plate capacitor charged to a potential difference V as shown in the figure. The forces on the two protons are identical.[1986-3 marks]**

**Ans.**True.When a parallel plate capacitor is charged to a potential difference V, a uniform electric field E-V / Jis produced between the plates. Let each of the proton, A and B, carry charge q.Force on a proton, A or B=qE Since q and E are same for each proton, the forces on them are identical.The statement is true

**85.A ring of radius R carries a uniformly distributed charge +Q. A point charge -q is placed on the axis of the ring at a distance 2R from the centre of the ring and released from rest. The particle executes a simple harmonic motion along the axis of the ring.Â [1988-2 marks]**

**Ans.**

The force is not proportional to displacement. The charge particle will not execute simple harmonic motion.The statement is false.**Note :** If x<< R, the charged particle will execute simple harmonic motion.

**86.An electric line of force in the x-y plane is given by the equation x ^{2} + y^{2} = 1. A particle with unit positive charge, initially at rest at the point x = l,y = 0 in the x-y plane, will move along the circular line of force.Â Â Â Â Â Â [1988-2 marks]**

**Ans.**

A unit positive charge is placed at A(1,0).Line of force is circular with radius =1.A line of force represents the path in an electric field along which a unit positive charge moves. The unit positive charge at A is already on the circular line of force. It will move along the circular line of force.The statement is true.

**Fill in the blanks type**

**87.Five identical capacitor Â plates, each of area A, areÂ arranged such that adjacent plates are at a distance d Â apart. The plates Â areÂ connected to a source of emfÂ V as shown in the figure.The charge on plate 1 is ……………. Â and on plate 4 is Â [1984-2 marks]**

**Ans.**Plates 1 and 2 form a parallel plate condenser. Plate 1 is connected to +ve terminal while plate 2 is conÂnected to negative terminal.

**88.Figure shows line of constant potential in a region in w’hich an electric field is present. The values of the potential are written in bracketsÂ Of the points A,B and C, the magnitude of the electric field is greatest at the point………[1984-2marks]**

**Ans.**The magnitude of electric field is greatest at the point where the lines of force are crowded most, being close to each other. At B, the separation beÂtween 10V and 20 V lines is the least, as is clear from the figure.Hence the electric field is greatest at B.

**89.Two small balls having equal positive charge Q (coulomb) on each are suspended by two insulating strings of equal length L(metre) from a hook fixed to a stand. The whole setup is taken in a satellite into space where there is no gravity (state of weightlessness). The angle between the twoÂ strings is ………….. Â and the tension in each string is……… ….newton.[1986-2 marks]
**

**Ans.**The two balls hang in gravity-free space in state of weightlessness in the satellite. There is only elecÂtrostatic force of repulsion between them. The balls will be repelled till the two strings are at 180Â°. The tension in each string will be equal to the electroÂstatic force between charges.

**90.Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference V. The battery is then disconnected and the region beween the plates of the capacitor C is completely filled with a material of dielectric constant K. The potential differenceÂ across the capacitors now becomes…………………[1989-2 marks]**

**Ans.**

**91.A point charge q moves from point P to point S along the path PQRS (figure) in a uniform electric field E pointing parallel toÂ the positive direction of the X-axis. The coordinates P,Q,R and S are (a,b,0), (2a,0,0), (a,b,0) and (0,0,0) respectively. The work done by the field in the above process is given by the expression Â [1989-2 marks]**

**Ans.**

**92.The electric potential V at any point x,y,z (all in metre) in space is given by V = 4x ^{2} volt. TheÂ electric field at the point (lm, 0, 2m) is………………. V/mÂ [1992-1 mark]**

**Ans.**

**93.Five point charges, each of value +q coulomb, are placed on five vertices of a regular hexagon of side L metre. The magnitude of the force on the point charge of value -q coulomb placed at the centre of the hexagon is …. newtonÂ [1992-1 mark]**

**Ans.**