An isolated sphere has a capacitance of 50pF. What would be the radius of the sphere?

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An isolated sphere has a capacitance of 50pF. What would be the radius of the sphere?

Options

(a) 90cm
(b) 45cm
(c) 11.50cm
(d) 5.75cm

Correct Answer:

45cm

Explanation:

As potential of spherical charge (Q) having radius r is given by V = (1 / 4πε₀) (Q / r)

Also, capacitance, C = Q / V = Q / { (1 / 4πε₀) (Q / r)} C = 4πε₀r

If C = 50 × 10⁻¹² F, then

Radius of the sphere r = 50 × 10⁻¹² / 4πε₀

= 50 × 10⁻¹² × 9 × 10⁹

= 50 × 9 × 10⁻³

= 450 × 10⁻³ m

= 0.450 m = 45 cm

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Topics: Electrostatics (146)
Subject: Physics (2479)

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