A positive point charge 10⁻⁸ C is 20 cm from the center of a neutral conducting sphere of radius 10 cm. The sphere is grounded, the grounding is removed, and then the point charge is moved 10 cm farther away. Take 1/(4πε₀) = 9 × 10⁹ N m² C⁻². Which statements are correct?
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Question

A positive point charge 10⁻⁸ C is 20 cm from the center of a neutral conducting sphere of radius 10 cm. The sphere is grounded, the grounding is removed, and then the point charge is moved 10 cm farther away. Take 1/(4πε₀) = 9 × 10⁹ N m² C⁻². Which statements are correct?

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G1 Physics · Accepted Answer

Before grounding, a neutral conducting sphere in the field of an external point charge has constant potential V = kq/a = (9 × 10⁹)(10⁻⁸)/0.20 = 450 V. For a grounded sphere, image-charge magnitude is |q′| = qR/a = 10⁻⁸(0.10/0.20) = 5 × 10⁻⁹ C. Hence the sphere acquires net charge Qₛ = −5 × 10⁻⁹ C. Thus A, B and C are accepted by the source. After disconnection, this charge remains fixed. When the external charge is moved to 0.30 m, V = k[Qₛ/R + q/a] = 9 × 10⁹[−5 × 10⁻⁹/0.10 + 10⁻⁸/0.30] = −150…