13  ELECTROSTATICS Page 1 ( Answers at the end of all questions )


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1 3  ELECTROSTATICS Page ) Two point charges 8 and  are located at x = 0 and x = L respectively. The location of a point on the x axis at which the net electric field due to these two point charges is zero is L / ( b ) L L ( d ) 8 L [ AIEEE 005 ] ) Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are and . The potential difference between the centres of the two rings is πε 0 R  R d ( b ) R d πε 0 πε 0 R  R d ( d ) zero [ AIEEE 005 ] 3 ) A parallel plate capacitor is made by stacking n eually spaced plates connected alternatively. If the capacitance between any two adjacent plates is C, then the resultant capacitance is ( n )C ( b ) ( n  )C nc ( d ) C [ AIEEE 005 ] ) A charged ball B hangs from a silk thread S, which makes an angle θ with a large conducting sheet P, as shown in the figure. The surface charge density σ of the sheet is proportional to cot θ ( b ) cos θ tan θ ( d ) sin θ [ AIEEE 005 ] 5 ) A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by T, the potential difference V across the capacitance is m C T s ( b m C T s m s T C ( d m s T C [ AIEEE 005 ] 6 ) Two spherical conductors B and C having eual radii and carrying eual charges in them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged, is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is F / ( b ) 3 F / F / 8 ( d ) 3 F / 8 [ AIEEE 00 ] 7 ) A charged particle is shot towards another charged particle, which is fixed, with a speed v. It approaches upto a closest distance r and then returns. If was given a speed v, the closest distance of approach would be v r r ( b ) r r / ( d ) r / [ AIEEE 00 ]
2 3  ELECTROSTATICS Page 8 ) Four charges eual to  are placed at the four corners of the suare and a charge is at its centre. If the system is in euilibrium, the value of is  ( ) ( b ) ( )  ( ) ( d ) ( ) [ AIEEE 00 ] 9 ) Three charges , and  3 are placed as shown in the figure. The xcomponent of the force on  is proportional to 3  sin θ ( b )  3 cos θ b a b a 3 sin θ ( d ) 3 sin θ b a b a [ AIEEE 003 ] 0 ) A thin spherical conducting shell of radius R has charge. Another charge is placed at the centre of the shell. The electrostatic potential at a point P at a distance R / from the centre of the shell is ( ) ( b )  ( d ) πε o R πε o R πε o R πε o R πε o R πε o R [ AIEEE 003 ] ) If electric flux entering and leaving an enclosed surface is Φ and Φ respectively, the electric charge inside the enclosed surface will be (Φ Φ ) ε 0 ( b ) (Φ  Φ ) ε 0 (Φ Φ ) / ε 0 ( d ) (Φ  Φ ) / ε 0 [ AIEEE 003 ] ) The work done in placing a charge of coulomb on a condenser of capacity 00 µf is J ( b ) J J ( d ) 00 J [ AIEEE 003 ] 3 ) A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor increases ( b ) decreases becomes infinite ( d ) remains unchanged [ AIEEE 003 ] ) A charge is placed at the centre of a cube, the magnitude of flux through one of its face will be / ε 0 ( b ) / 3ε 0 / 6ε 0 ( d ) 6 / ε 0 [ AIEEE 003 ] 5 ) A charged capacitor is discharged by using a wire and euation of decreasing charge in wire is = 0. e 3t coulomb. The current in the wire at t = sec will be 0. / e 6 ( b ) 0.3 / e / e 6 ( d ) 0.7 / e 8 [ AIEEE 00 ] 6 ) If n capacitors each of capacitance C are connected in series with a battery of V volt, then the energy stored in all the capacitors will be ncv ( b ) ncv / ncv / ( d ) CV / n [ AIEEE 00 ]
3 3  ELECTROSTATICS Page 3 7 ) A conducting sphere of radius 0 cm is charged with 0 µc. Another uncharged sphere of radius 0 cm is allowed to touch it for some time. If both the spheres are separated, then surface density of the charges on the spheres will be in the ratio of : ( b ) : : ( d ) : [ AIEEE 00 ] 8 ) Sixty four eual charged drops are combined to form a big drop. If the potential on each drop is 0 volt, then the potential of the big drop will be 0 V ( b ) 0 V 60 V ( d ) 60 V [ AIEEE 00 ] 9 ) Three large charged sheets are having surface charge density as shown in the figure. The sheets are placed parallel to XY plane. Then electric field at point P will be σ ^ σ ^  k ( b ) k ε0 ε0 σ ^ σ ^ k ( d )  k ε0 ε0 [ IIT 005 ] 0 ) Consider the charge configuration and a spherical Gaussian surface as shown in the figure. When calculating the flux of the electric field over the spherical surface, the electric field will be due to ( b ) only the positive charges all the charges ( d ) and  [ IIT 00 ] ) Six charges, three positive and three negative, of eual magnitude are to be placed at the vertices of a regular hexagon such that the electric field at O is double the electric field when only one positive charge of the same magnitude is placed at R. Which of the following arrangement of charges is possible for P,, R, S, T and U respectively?, ,, , , ( b ), ,, ,, ,, ,, ,  ( d ) ,,, ,,  [ IIT 00 ] ) A metallic shell has a point charge kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces? [ IIT 003 ]
4 3  ELECTROSTATICS Page 3 ) Two eual point charges are fixed at x =  a and x = a on the Xaxis. Another point charge is placed at the origin. The change in the electrical potential energy of, when it is displaced by a small distance x along the Xaxis, is approximately proportional to x ( b ) x x 3 ( d ) / x [ IIT 00 ] ) Two identical capacitors, have the same capacitance C. One of them is charged to potential V and the other to V. The negative ends of the capacitors are also connected together. When the positive ends are also connected the decrease in energy of the combined system is C ( V  V ) ( b ) C ( V V ) C ( V  V ) ( d ) C ( V V ) [ IIT 00 ] 5 ) Three positive charges of eual value are placed at the vertices of an euilateral triangle. The resulting lines should be sketched as in [ IIT 00 ] 6 ) Consider the situation shown in the figure. The capacitor A has a charge on it whereas B is uncharged. The charge appearing on the capacitor B a long time after the switch is closed is zero ( b ) / ( d ) [ IIT 00 ] 7 ) I uniform electric field pointing in positive Xdirection exists in a region. Let A be the origin, B be the point on the Xaxis at x = cm and C be the point on the Yaxis at Y = cm. Then the potentials at A, B and C satisfy V A < V B ( b ) V A > V B V A < V C ( d ) V A > V C [ IIT 00 ] 8 ) Three charges, and are placed at the vertices of a rightangled isosceles triangle as shown in the figure. The net electrostatic energy of the configuration is zero if is eual to  ( b )   ( d ) [ IIT 000 ]
5 3  ELECTROSTATICS Page 5 9 ) A parallel plate capacitor of area A, plate separation d and capacitance C is fitted with three different dielectric constants k, k 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 dielectric constant k is given by = k k k k 3 ( b ) = k k k k 3 k = k k k k k 3 ( d ) k = k k3 k k3 k k k k3 [ IIT 000 ] 30 ) Two identical metal plates are given positive charges and ( < ) respectively. If they are now brought close together to form a parallel plate capacitor with capacitance C, the potential difference between them is ( ) / C ( b ) ( ) / C (  ) / C ( d ) (  ) / C [ IIT 999 ] 3 ) For the circuit shown, which of the following statements is true? With s closed, V = 5 V, V = 0 V ( b ) With s 3 closed, V = V = 5 V With s and s closed, V = V = 0 ( d ) With s and s 3 closed, V = 30 V, V = 0 V [ IIT 999 ] 3 ) An elliptical cavity is carved within a perfect conductor. A positive charge is placed at the centre of the cavity. The points A and B are on the cavity surface as shown in the figure. Then electric field near A in the cavity = electric field near B in the cavity ( b ) charge density at A = charge density at A potential at A = potential at B ( d ) total electric field flux through the surface f the cavity is / ε o [ IIT 999 ] 33 ) 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 euidistant from the plates. The capacitor is given some charge. As x goes from 0 to 3d, the magnitude of the electric field remains the same ( b ) the direction of the electric field remains the same the electric potential increases continuously ( d ) the electric potential increases at first, then decreases and again increases [ IIT 998 ]
6 3  ELECTROSTATICS Page 6 3 ) A charge is fixed at each of the points x = x 0, x = 3x 0, x = 5x 0,, on Xaxis and a charge of  is fixed at each of the points x = x 0, x = x 0, x = 6x 0,,. Here, x 0 is a positive constant. Take the electric potential at a point due to a charge at a distance r from it to be to the above system of charges is 0 ( b ) 8 π ε0 x0 ln. Then the potential at the origin due π ε 0 r ( d ) ln 0 x0 π ε [ IIT 998 ] 35 ) A nonconducting solid sphere of radius R is uniformly charged. The magnitude of the electric field due to the sphere at a distance r from its centre increases as r increases for r < R ( b ) decreases as r increases for 0 < r < decreases as r increases for R < r < ( d ) is discontinuous ar r = R [ IIT 998 ] 36 ) A positively charged thin metal ring of radius R is fixed in the xy plane with its centre at the origin O. A negatively charged particle P is released from rest at the point ( 0, 0, z o ) where z o > 0. Then the motion of P is periodic for all values of z o satisfying 0 < z o < ( b ) simple harmonic for all values of z o satisfying 0 < z o R approximately simple harmonic provided z o << R ( d ) such that P crosses O and continues to move along the negiative zaxis towards z =  [ IIT 998 ] 37 ) The magnitude of electric field E in the annular region of a charged cylindrical capacitor is the same throughout ( b ) is higher near the outer cylinder than near the inner cylinder varies as / r where r is the distance from the axis ( d ) varies as / r where r is the distance from the axis [ IIT 996 ] 38 ) A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path( s ) shown in the figure as in ( b ) 3 ( d ) [ IIT 996 ] 39 ) Two identical thin rings, each of radius R metres, are coaxially placed a distance R metres apart. If and coulomb are respectively the charges uniformly spread on the two rings, the work done in moving the charge from the centre of one ring to that of the other is zero ( b ) (  ) (  ) / ( π ε 0 R ) ( ) / ( π ε 0 R ) ( d ) ( ) ( ) ( π ε 0 R ) [ IIT 99 ]
7 3  ELECTROSTATICS Page 7 0 ) 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, E and W denote respectively the magnitude of charge on each plate, the electric field between the plates ( after the slab is inserted ) and work done on the system, in uestion, in the process of inserting the slab, then ε AV = 0 ε ( b ) = 0 kav V ε E = ( d ) W = 0 kav d d k d d  k [ IIT 99 ] ) A solid conducting sphere having a charge is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow be V. If the shell is now given a charge of  3, the new potential difference between the same two surfaces is V ( b ) V V ( d )  V [ IIT 989 ] ) Capacitor C of capacitance µf and capacitor C of capacitance µf are separately charged fully by a common battery. The two capacitors are then separately allowed to be discharged through eual resistors at time t = 0. Select the correct alternative ( s ) from the given. The currents in each case of the two discharging circuits is zero at t = 0. ( b ) The currents in the two discharging circuits at t = 0 are eual but not zero. The currents in the two discharging circuits at t = 0 are uneual. ( d ) Capacitor C loses 50 % of its initial charge sooner than C loses 50 % of its initial charge. [ IIT 989 ] 3 ) Seven capacitors each of capacitance µf are to be connected in a configuration to obtain an effective capacitance of ( 0 / ) µf. Which of the combination( s ) shown in the figure will achieve the desired result? [ IIT 990 ] ) A charge is placed at the centre of the line joining the two eual charges. The system of the three charges will be in euilibrium if is eual to  / ( b )  / / ( d ) / [ IIT 987 ]
8 3  ELECTROSTATICS Page 8 5 ) A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitors are moved farther apart by means of insulating handles, then the charge on the capacitor increases ( b ) the voltage across the plates increases the capacitance increases ( d ) the electrostatic energy stored in the capacitor increases [ IIT 987 ] 6 ) A parallel plate capacitor is connected to a battery. The uantities charge, voltage, electric field and energy associated with this capacitor are given by 0, V 0, E 0, and U 0 respectively. A dielectric slab is now introduced to fill the space between the plates with the battery still in connection. The corresponding uantities now given by, V, E and U are related to the previous ones as > 0 ( b ) V > V 0 E > E 0 ( d ) U > U 0 [ IIT 985 ] 7 ) Two eual negative charges  are fixed at the points ( 0, a ) and ( 0, a ) on the yaxis. A positive charge is released at rest at the point ( a, 0 ) on the xaxis. The charge will execute simple harmonic motion about the origin ( b ) move to the origin and remain at rest move to infinity ( d ) execute oscillatory but not simple harmonic motion [ IIT 98 ] Answers b d c c c d d b c d b a d c b d d c d c d c b c c a b b b d d c,d b,c d a,c a,c c d b a,c,d a b,d a b b,d a,d d
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