A positive point charge of 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 (where is the permittivity of free space), which of the following statements is/are correct:
- A
Before the grounding, the electrostatic potential of the sphere is 450 V.
- B
Charge flowing from the sphere to the ground because of grounding is C.
- C
After the grounding is removed, the charge on the sphere is C.
- D
The final electrostatic potential of the sphere is 300 V.
Let C, m, m (initial point-charge distance from centre).
(A) Potential of the neutral sphere before grounding: the induced charges sum to zero, contributing zero net potential at the centre; only the external point charge contributes there, and the whole conductor is at the centre's potential.
V. (A) is correct.
(B), (C) After grounding: the sphere's potential is forced to zero. If is the new charge on the sphere,
So C flowed from earth to sphere (equivalently, C from sphere to ground). Both (B) and (C) are correct.
(D) Final potential after grounding removed and charge moved to m: the sphere now keeps C fixed. The potential at the centre (and thus on the sphere) becomes
V V. (D) is incorrect.
Correct options are (A), (B), (C).