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Electrostatics — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsElectrostatics3 Marks
Question
A system consisting of a charged spherical shell and an electron has negative electric potential energy $U=-15 \times 10^{-20} J$, with $U(\infty)=0$.
(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 $U(\infty)=0$, the potential energy of two point charges $q_1$ and $q_2$ a distance $r_{21}$ apart is
$
U =\frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_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 $U ^{\prime}= \pm 15 \times 10^{-20} J$

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