Page 1 1 PRACTICE SET: ELECTROSTATICS LEVEL: Conceptual & Advanced Level- SET-1 1. A small point mass m has a charge q, which is constrained to move inside a narrow frictionless cylinder. At the base of the cylinder is a point mass of charge Q having the same sign as q. If the mass m is displaced by a small amount from its equilibrium position and released, it will exhibit simple harmonic motion. Find the angular frequency of the mass. 2. A small bead of mass m having charge –q is constrained to move along a frictionless wire. A positive charge Q lies at a distance L from the wire. Initially bead is just above charge +Q. Show that if the bead is displaced a distance x, where x < < L, and released, it will exhibit simple harmonic motion. Obtain an expression for the time period of simple harmonic motion. 3. A charged particle q of mass (m) is in equilibrium at a height h from a horizontal infinite line charge with uniform linear charge density ?. The charge lies in the vertical plane containing the line charge. If the particle is displaced slightly (vertically). Prove that the motion of the charged particle will be simple harmonic and find its time period. (write time period of oscillation. 4. An infinitely long straight conductor carrying a charge density ? = 100 ?C/m and a point charge Q = ?1600 ?C are placed at a distance 1m on x ?y plane as shown in the figure. (a) Plot schematically (without a definite scale) the variation of electric field on X-axis in the region I, II and III. (b) Find the coordinate of the points on the X-axis where electric field is zero and locate them on the graph. 5. A small cork ball A of mass m is suspended by a thread of length l. Another ball B is fixed at a distance l from point of suspension and distance l/2 from thread when it is vertical, as shown in figure. Ball A and B, each has positive charge q. Ball A is held by an external force such that the thread remains vertical. When ball A is released from rest, thread deflects through a maximum angle of ? = 30 0 , calculate m in terms of the other parameters. ? Y 1m Q X I II III m q y 0 Q A B l l/2 ? O ? ? L +Q m -q X x Page 2 1 PRACTICE SET: ELECTROSTATICS LEVEL: Conceptual & Advanced Level- SET-1 1. A small point mass m has a charge q, which is constrained to move inside a narrow frictionless cylinder. At the base of the cylinder is a point mass of charge Q having the same sign as q. If the mass m is displaced by a small amount from its equilibrium position and released, it will exhibit simple harmonic motion. Find the angular frequency of the mass. 2. A small bead of mass m having charge –q is constrained to move along a frictionless wire. A positive charge Q lies at a distance L from the wire. Initially bead is just above charge +Q. Show that if the bead is displaced a distance x, where x < < L, and released, it will exhibit simple harmonic motion. Obtain an expression for the time period of simple harmonic motion. 3. A charged particle q of mass (m) is in equilibrium at a height h from a horizontal infinite line charge with uniform linear charge density ?. The charge lies in the vertical plane containing the line charge. If the particle is displaced slightly (vertically). Prove that the motion of the charged particle will be simple harmonic and find its time period. (write time period of oscillation. 4. An infinitely long straight conductor carrying a charge density ? = 100 ?C/m and a point charge Q = ?1600 ?C are placed at a distance 1m on x ?y plane as shown in the figure. (a) Plot schematically (without a definite scale) the variation of electric field on X-axis in the region I, II and III. (b) Find the coordinate of the points on the X-axis where electric field is zero and locate them on the graph. 5. A small cork ball A of mass m is suspended by a thread of length l. Another ball B is fixed at a distance l from point of suspension and distance l/2 from thread when it is vertical, as shown in figure. Ball A and B, each has positive charge q. Ball A is held by an external force such that the thread remains vertical. When ball A is released from rest, thread deflects through a maximum angle of ? = 30 0 , calculate m in terms of the other parameters. ? Y 1m Q X I II III m q y 0 Q A B l l/2 ? O ? ? L +Q m -q X x 2 PRACTICE SET: ELECTROSTATICS LEVEL: Conceptual & Advanced Level- SET-1 6. A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E ? is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring. 7. A positive charge +Q is fixed at a point A. Another positively charged particle of mass m and charge +q is projected from a point B with velocity u as shown in the fig. the point B is at large distance from A and at distance ‘d’ from the line AC. The initial velocity is parallel to the line AC. The point C is at very large distance from A. Find the minimum distance (in meter) of +q from +Q during the motion. Take Qq = 4 ? ? 0 mu 2 d and d = ? ? 21 ? meter. 8. Two small identical balls lying on a horizontal plane are connected by a weightless spring. One ball (ball 2) is fixed at O and the other (ball 1) is fee. The balls are charged identically as a result of which the spring length increases ? = 2 times. Determine the change in frequency. + + 2 1 O 9. Two small balls having the same mass and charge and located on the same vertical at heights h 1 and h 2 are thrown in the same direction along the horizontal at the same velocity v. The first ball touches the ground at a horizontal distance R from the initial vertical position. At what height h 2 will the second ball be at this instant? Neglect any frictional resistance of air and the effect of any induced charges on the ground. ANSWERS 1. 0 2g y 2. 3 0 4 2 mL Qq ?? ? 3. 2 ? 2 2 mh kq ? 4. (b) ? 4 24 m 5. 9 2 9 10 ( ) 2 (2 3) qx xg ?? ? 6. 2 4 mr qE ? 7. d(1 + 2 ) 8. frequency increases 2 times. 9. 2 12 R h h g v ?? ?? ?? ?? B u d A C +QRead More

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