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AL-MC-Electrostatics / p.1 1. (88-I-31) 3. (89-I-25) Two large metal plates A, B are oppositely charged The diagram shows points of equal potential joined and placed a small distance apart. A piece of metal as equipotential lines. Which of the following M is placed centrally between the plates. Which of statements is/are correct? the following graphs shows the variation of electric field intensity E from A to B? (1) The electric field at P is in a direction tangential to the line passing through P. (2) The electric field is the same at the points P and Q. (1) Work has to be done in moving an electron from point P to point R. 2. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only (88-I-33) 4. (89-I-26) An isolated spherical conductor of radius r is charged to a potential V. The total electrical energy stored is A potential difference V is maintained between plates X and Y, separated by a distance h. A particle of mass m and positive charge q enters the region between X and Y through the hole H with negligible velocity. If it makes no collision on the way, it will strike X with kinetic energy A. mgh. B. qV. C. qV + mgh. D. qV – mgh. E. mgh – qV. A. V 2 /(80 r ). B. V 2 /( 40 r ). C. V 2 /( 20 r ). D. V 2 (20 r ). E. V 2 (40 r ). AL-MC-Electrostatics / p.2 5. (89-I-30) The arrangement above shows two concentric hollow metal spheres of inner radius b and outer radius a. A charge + Q is given to the inner sphere and the outer sphere is earthed. What is the work done in bringing a small positive charge q from infinity to the surface of the inner sphere? A particle carrying negative charge is free to move in a uniform electric field E. If the particle starts with a certain velocity from points X, which of the paths shown could represent the route which the particle would follow from X to Y? A. I and II only B. I and IV ony C. II and III only D. III and IV only E. I, II, III and IV 8. 6. A. zero B. qQ /( 40 a) C. qQ /( 40b) D. qQ /40 a b E. qQ(1/ b 1/ a) /( 40 ) (90-I-29) (90-I-27) A light conducting sphere is hanged from a long insulating thread between oppositely charged metal plates connected to a high voltage supply. If the sphere is given a positive charge, it will A. move to the positive plate and stick to it. B. move to the negative plate and stick to it. C. remain still. D. oscillate, touching each plate in turn, beginning with the negative plate. E. oscillate, touching each plate in turn, beginning with the positive plate. 7. (90-I-28) A uniformly charged wire has the form of a P1 and P2 are two circular loop of radius b. points on the axis of the loop. b from the loop centre and from the loop centre. At are P1 is at a distance P2 is at a distance 2 b P1 , P2 , the potentials V1 ,V2 respectively. V2 /V1 is equal to A. 1/3 B. 2/5 C. 1/2 D. E. 2/ 5 4 AL-MC-Electrostatics / p.3 9. (91-I-31) Which of the graphs below best represents the variation of electrical potential V with distance r from the centre of a charged hollow metal sphere of external radius a? 12. 10. (92-I-27) (93-I-29) A positively-charged metal sphere A of radius a is How do the two physical quantities below change joined by a conducting wire to an uncharged metal along the direction indicated by an electric field line sphere B of radius b placed far away from the first from a point positive charge? sphere. The ratio of the surface charge density on sphere A to that on sphere B is (1) electric field intensity E (2) potential V A. b/a B. b2/a2 A. Only E will increase C. a/b B. Only V will increase D. a2/ b2 C. Both E and V will increase D. Both E and V will decrease E. b/a E. Both E and V will remain constant 11. (93-I-28) An uncharged metal sphere is placed in a uniform electric field. Which of the following best represents the electric field pattern around the metal sphere? AL-MC-Electrostatics / p.4 13. (93-I-35) 15. (94-IIA-24) Two insulated parallel metal plates are connected to X, Y are two different points in an electric field. A the terminals of an EHT. When a charged small charged object is released from rest at X. aluminium foil strip is placed between the plates, Which of the following conditions would ensure that deflection of the foil is observed as shown. the charged object will NOT pass through Y? A. The electric field at Y is zero. B. The electric field at Y is stronger than that at X. C. The electric field between X and Y is not zero. D. The electric potentials at X and Y are equal. E. Which of the following statements is/are true? The electric potential difference between X and Y is not zero. (1) The charge on the foil is negative. (2) Deflection of the foil increases if the Which of the following pairs of physical quantities separation between the plates decreases. is/are both scalars? (3) 16. (94-IIA-25) When moving the foil towards the positive plate, the deflection of the foil increases. (1) work done and electric field intensity (2) pressure and force (3) charge and electric potential A. (1) only B. (3) only C. (1) and (2) only A. (1) only D. (2) and (3) only B. (3) only E. (1), (2) and (3) C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) 14. (94-IIA-23) A 10 W light bulb gives a certain illumination on a surface 1.5 m away. At what distance would a 40 W light bulb give the same illumination? (You may regard a light bulb as a point source) A. 1.5 m B. 3.0 m C. 6.0 m D. 12.0 m E. 24.0 m AL-MC-Electrostatics / p.5 17. (94-IIA-27) 19. (95-IIA-27) The electric potential energy of a system of charges at infinitely large distances from one another is taken to be zero. What is the electric potential energy stored in a system of four charges, each of A, B, C, D are four points on a straight line as shown. +1 C, placed at the vertices of a square with length A point charge +Q is fixed at A. When another point of side 1 m? ( o = permittivity of vacuum) charge –Q is moved from B to C, which of the A. B. C. D. E. 3 following quantities will increase? (1) o charges. (2) 1 1 (2 ) o 2 (3) The electric potential at the point D. A. (1) only o B. (3) only C. (1) and (2) only 5 D. (2) and (3) only 4 o 4o The magnitude of the electric field strength at the point D. 1 1 The electric potential energy of the system of E. (1), (2) and (3) (4 2 ) 20. (96-IIA-16) The straight lines in the diagram represent electric field lines. Which of the following statements about 18. (95-IIA-26) this electric field is/are correct? Two uncharged metal spheres, A and B, supported by insulating stands are placed side by side but not touching each other. A student places a positively-charged rod near sphere A and he touches sphere B with his finger momentarily. When the rod is removed afterwards, what are the signs of the (1) charges induced on the spheres? A stationary negative charge placed at Q tends to move to P. (2) The electric field strength at P is stronger than that at Q. Sphere A Sphere B A. positive neutral B. negative negative C. negative neutral D. neutral positive A. (1) only E. neutral negative B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) (3) Work has to be done in moving a negative charge from R to P. AL-MC-Electrostatics / p.6 21. (96-IIA-23) (1) the mass of the charged particle. Five identical point charges, each of charge Q, are (2) The width of the gap. fixed evenly on a circle of radius r. How much work (3) The potential difference between the plates. has to be done to bring another point charge Q from infinity to the centre of the circle? A. (1) only ( 0 = permittivity of free space) B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) A. B. C. zero 5Q 4 0 r 24. (98-IIA-22) Which of the following graphs shows correctly the 5Q 2 40 r D. 5Q 2 40 r 2 E. 5Q 40 r 2 relationship between the energy E stored in an isolated conducting sphere and the charge Q on it? 22. (97-IIA-22) A metal sphere is charged to a potential of 100 V. If the charge density on its surface is 6.0 x10 9 Cm 2 , find the radius of the sphere. (Given : permittivity of free space = 8.85 x10 12 Fm 1 ) A. 0.04 m 25. (99-IIA-21) B. 0.15 m Which of the following statements about electric C. 0.21 m field lines is incorrect? D. 0.35 m E. 0.60 m A. They are closest where the field is strongest. 23. (97-IIA-28) B. A charged particle is accelerated across the gap between two parallel metal plates maintained at a equipotential lines. C. certain potential difference in a vacuum. Assuming there is no gravitational force, the energy acquired They are always perpendicular to They always point from high electric potential to low electric potential. D. Work has to be done in moving an by the charged particle in crossing the gap depends electron along the direction of a field on line. E. They tend to attract one another. AL-MC-Electrostatics / p.7 26. (00-IIA-21) 28. (00-IIA-26) Two parallel plates are connected to an E.H.T. of 4.5 kV. Electric breakdown occurs when the separation of the plates is reduced to 1.5 mm. In the above arrangement, two small test charges Estimate the maximum acceleration of an electron +q and +2q are brought from infinity to the between the plates. positions shown. The two charges are collinear (Given: charge of an electron = 1.6 10 with another charge +Q and their mutual mass of an electron = separation is d. Which of the following statements 19 C; 9.1 10 31 kg ) is/are correct? A. (1) (2) Charge +q is at a higher potential than B. charge +2q. C. The work done in bringing the charges +q D. and +2q from infinity to their respective E. 4.0 10 7 m s-2 1.0 10 9 m s-2 1.2 1012 m s-2 1.6 1015 m s-2 5.3 1017 m s-2 positions is the same. (3) The potential energy of the system would increase if d decreases. 29. (01-IIA-20) Two insulated uncharged metal spheres X and Y are in contact with each other. A positively charged rod 27. A. (1) only is brought near X without any contact while sphere B. (3) only X is earthed as shown. C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) (00-IIA-22) At steady state, which of the following descriptions is/are correct? (1) Sphere X gains electrons. (2) Sphere Y loses electrons. (3) Sphere X acquires a negative electric The figure shows a pattern of electric field lines in which P, Q and R are points marked on one of the field lines with PQ = QR. If the potential at P is potential. (4) Sphere Y acquires a positive electric potential. 0 V, which of the following can give the possible potentials at Q and at R? Potential at Q Potential at R A. B. C. -200 V -200 V -200 V -450 V -400 V -350 V D. +200 V +350 V E. +200 V +450 V A. (1) only B. (1) and (2) only C. (1) and (3) only D. (2) and (4) only E. (1), (2), (3) and (4) AL-MC-Electrostatics / p.8 30. (02-IIA-20) 32. In the above figure the solid lines represent part of an electric field due to fixed point charge Q (not shown in the figure). A charge particle q, subjected (03-IIB-23) The magnitudes of the charges on two identical small metal spheres are in the ratio 5:1. The Coulomb interaction force between them is F1. If they are brought into contact and then separated to their respective original positions, the Coulomb interaction force between them becomes F2. Which of the following is/are possible magnitude ratios of F1:F2? only to electric force in the field, travels along the (1) 5 : 9 (2) 5 : 4 (3) 5 : 2 dotted curve shown. Which of the following conclusions can be shown? A. q is travelling from X to Y B. The charge of q has the same sign as that of Q C. q has a greater speed at X than at Y D. The electric potential at X due to Q is higher than that at Y 31. (02-IIA-21) The above figure shows an electrons entering a uniform field which may be electric or magnetic. Which of the following description about the subsequent motion of the electron is correct? A. Only in a magnetic field can the electron be B. deflected by more than 90 Only in an electric field does the force depend on the magnitude of the charge on the electron C. Whether the field is electric or magnetic, the speed of the electron will increase D. Whether the field is electric or magnetic, the magnitude and direction of the force acting on the electron are constant. A. B. C. D. (1) only (3) only (1) and (2) only (2) and (3) only AL-MC-Electrostatics / p.9 33. (03-IIB-24) In the figure, the solid curves are concentric circles representing set of equipotential surfaces in an electric field. The dotted curve ABC represents the path of a charged particle moving in the field. Which of the following deductions from the figure is/are correct? (Neglect the effects of gravity.) (1) (2) (3) A. B. C. D. The charged particle is always repelled from the centre of the concentric circles. The speed of the charged particle at A is equal to that at C. The kinetic energy of the charged particle at B is grater than that at A. (1) only (3) only (1) and (2) only (2) and (3) only