Question

How do the charges compare when two objects are charged through friction? The objects become oppositely charged and have equal amounts of charge. The objects become positively charged and have equal amounts of charge. The objects become negatively charged and have different amounts of charge. The objects become oppositely charged and have different amounts of charge.

Answer 1

If both objects started with no charge, they would carry opposite charges of the same magnitude after rubbing.

Explanation:

When one insulator is rubbed against another, some electrons on one insulator might travel to the surface of the other insulator. Electrons are neither lost nor created in this process- they are just moved from one surface to the other.

Let the two insulators in this question be denoted as
`A` and
`B`. Assume that both insulators were initially not charged.

Let
`{\rm e}` denote the fundamental charge. Each electron carries a negative charge of
`(-1\; {\rm e})`. Assume that
`n` electrons are moved from insulator
`A\!` to insulator
`B\!`:

• Insulator
  `A\!\!` would now have
  `n\!` fewer electrons than it used to do. Thus, the charge on insulator
  `A\!` would have been reduced by
  `n * (-1\; {\rm e})`. Since insulator
  `A` started with no charge, it would now carry a charge of
  `0 - n * (-1 \; {\rm e}) = n\; {\rm e}`.
• Insulator
  `B` would now have
  `n` more electrons than it used to do. The charge on insulator
  `B\!` would have increased by
  `n * (-1\; {\rm e})`. Since insulator
  `B` started with no charge, it would now carry a charge of
  `0 + n* (-1\; {\rm e}) = (-n\; {\rm e})`.

In other words, the insulator that lost some electrons (which are negatively charged) now carries less negative charge and becomes positively charged. In contrast, the insulator that gained some electrons now carries more negatively charge becomes negatively charged.

The amount of electrons on the two objects combined stays unchanged. Thus, the amount of charge one insulator lost is equal to what the other insulator gained. Therefore, the sign of the charge on the two insulators would be different, but the magnitude (absolute value) of the charge would be equal.

Therefore, the two objects would be oppositely charged, with the magnitude of the charge on them being equal.