A positive point charge of 10-8 C is kept at a distance of 20 cm from the center of a neutral conducting sphere of radius 10 cm. The sphere is then grounded and the charge on the sphere is measured. The grounding is then removed and subsequently the point charge is moved by a distance of 10 cm further away from the center of the sphere along the radial direction. Taking 14 0=9 109 Nm2/C2 (where 0 is the permittivity of free space), which of the following statements is/are correct:
- Before the grounding, the electrostatic potential of the sphere is 450 V.
- Charge flowing from the sphere to the ground because of grounding is 5 10-9 C.
- After the grounding is removed, the charge on the sphere is -5 10-9 C.
- The final electrostatic potential of the sphere is 300 V.
Answer
(1) Before the grounding, the electrostatic potential of the sphere is 450 V., (2) Charge flowing from the sphere to the ground because of grounding is 5 10-9 C., (3) After the grounding is removed, the charge on the sphere is -5 10-9 C.
Solution
Potential of the sphere = potential at its centre = kqd+ kQR.
(A) Neutral: V= 9 109 10-80.2=450 V. Correct.
Grounded: kq0.2+ kQ0.1=0 Q=-5 10-9 C, i.e. 5 10-9 C of positive charge flows from sphere to ground. (B) correct.
Removing the ground leaves Q=-5 10-9 C. (C) correct.
Final: V=9 109 ( -5 10-90.1+ 10-80.3 )=-450+300=-150 V. (D) wrong.
Answer: (A), (B), (C)