Question

3. An isolated metal sphere of radius 'r' is given a charge' q'. The potential energy of the sphere is

Answer 1

Given info : An isolated metal sphere of radius r is given a charge q.

solution : method 1 : The potential energy of the sphere is ...

solution : The potential energy of the sphere, U = q²/2C,

capacitance of sphere = 4πε₀r

so, potential energy of sphere = q²/2(4πε₀r)

= q²/8πε₀r

method 2 : potential at the surface of sphere , V = kq/r [ from moves from infinity to the surface of sphere, so V_∞ = 0 ]

now, potential energy of sphere = work done to accumulate charge q = Vdq

= kq/r dq

= k/r∫ q dq

= kq²/2r

= q²/8πε₀r

Therefore the potential energy of sphere is q²/8πε₀r.

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