Question

two students are experimenting with two objects — a neutral metal sphere and a negatively - charged aluminum pie plate. they momentarily touch the pie plate to the sphere and pull it away. the metal sphere becomes charged negatively. the pie plate remains negatively - charged, but has less excess negative charge than it previously had. complete the analysis of this situation.
before
after
#p⁺ = #e⁻
#p⁺ = #e⁻
#p⁺ = #e⁻
#p⁺ = #e⁻
#p⁺ > #e⁻
#p⁺ > #e⁻
#p⁺ > #e⁻
#p⁺ > #e⁻
#p⁺ < #e⁻
#p⁺ < #e⁻
#p⁺ < #e⁻
#p⁺ < #e⁻
how did the metal sphere become charged?

Explanation:

When the negatively - charged pie plate touches the neutral metal sphere, electrons (negative charges) are transferred from the pie plate to the sphere. Since the sphere was neutral initially (\(\#p^{+}=\#e^{-}\)), after gaining electrons, \(\#p^{+}<\#e^{-}\). The pie plate had an excess of electrons (\(\#p^{+}<\#e^{-}\)) before the contact. When some electrons are transferred to the sphere, it still has \(\#p^{+}<\#e^{-}\) (but fewer excess electrons than before).

Answer:

Before: Sphere - \(\#p^{+}=\#e^{-}\), Pie plate - \(\#p^{+}<\#e^{-}\)
After: Sphere - \(\#p^{+}<\#e^{-}\), Pie plate - \(\#p^{+}<\#e^{-}\)