A system consisting of a charged spherical shell and an electron has

1.	A system consisting of a charged spherical shell and an electron has negative electric potential energy U = -15 × 10-20 J, with U(∞) = 0.(a) What is the sign of the charge on the shell? (b) If the electron is replaced by a proton, what would be the electric potential energy of the new system?
Answer» A charged spherical conductor is equivalent to a point charge at its centre. For U(∞) = 0, the potential energy of two point charges q₁ and q₂ a distance r apart is U = \(\cfrac1{4πε_0}\)\(\cfrac{q_1q_2}{r_{21}}\) Since the FE of the charged shell and electron system is negative, the shell must be positively charged, electron being negatively charged. If the electron is replaced by a proton, the PE of the new system would be positive equal to U’ = ±15 × 10^-20 J.

A system consisting of a charged spherical shell and an electron has negative electric potential energy U = -15 × 10-20 J, with U(∞) = 0.(a) What is the sign of the charge on the shell? (b) If the electron is replaced by a proton, what would be the electric potential energy of the new system?

Answer»

A charged spherical conductor is equivalent to a point charge at its centre. For U(∞) = 0, the potential energy of two point charges q₁ and q₂ a distance r apart is

U = \(\cfrac1{4πε_0}\)\(\cfrac{q_1q_2}{r_{21}}\)

Since the FE of the charged shell and electron system is negative, the shell must be positively charged, electron being negatively charged.

If the electron is replaced by a proton, the PE of the new system would be positive equal to

U’ = ±15 × 10^-20 J.

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A system consisting of a charged spherical shell and an electron has negative electric potential energy U = -15 × 10-20 J, with U(∞) = 0.(a) What is the sign of the charge on the shell? (b) If the electron is replaced by a proton, what would be the electric potential energy of the new system?

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