Question

An electrically neutral penny is charged by induction to +5.5 LaTeX: \muμC. After charging, is the penny now more massive or less massive, and what is its change in mass? Group of answer choices

More massive, 3.4E13 kg

Less massive, 3.1E-17 kg

More massive, 3.1E-17 kg

Less massive, 3.4E13 kg

More massive, 3.1E-12 kg

Answer 1

The charge induced on the penny by induction=Q=5.5*10^-6 C

In the process of induction, since the penny is charged positively, the eletrons from the penny have left and therefore positive charge has been induced. To explain the process in short, when a negatively charged object is brought close to a neutral conductor (here penny), the electrons and protons in the penny redistribute such that the electrons are away from the object and protons are near the object. After this when the conductor is grounded, the electrons leave the conductor thereby creating positive charge.

Since the electrons leave the conductor, the mass of conductor would reduce. Let us determine the number of electrons that left.

Total charge induced=+5.5*10^-6 C

Charge on one electron=qe=-1.6*10^-19 C

Number of electrons that left the penny=n=5.5*10^-6/(1.6*10^-19)=3.4375*10^13

Mass of one electron=9.109*10^-31 kg

Mass of n electrons=3.4375*10^13*9.109*10^-31=3.13*10^-17 kg

Therefore, penny become lighter or less massive by 3.1*10^-17 kg

Second option is correct