Question

Two charged particles are near each other – the charge magnitudes are +3 uC and +7 uC, respectively. The electrostatic force between these charges is 25 N. A charged particle of -1 uC is added to both of the original two charges. What is the electrostatic force between the two charged particles after the -1 uC charge is added?

Answer 1

Approximately
`14\; {\rm N}`.

Step-by-step explanation:

By Coulomb's Law, the magnitude of the electrostatic force between two charges is proportional to the product of the magnitudes of the two charges.

For example, consider charges of magnitude
`q_(1)` and
`q_(2)` that are apart from one another by a distance of
`r` in between. Let
`k` denote Coulomb's constant. By Coulomb's Law, the magnitude of electrostatic force between the two charges would be:

`\displaystyle F = (k\, q_(1)\, q_(2))/(r^(2))`.

In this question, the product of the magnitude of the two charges was originally
`3\; {\rm \mu C} * 7\; {\rm \mu C} = 21\; {\rm (\mu C)^(2)}`. After
`(-1\; {\rm \mu C})` is added to each charge, product of the magnitude of the two charges would become
`(3 - 1)\; {\rm \mu C} * (7 - 1)\; {\rm \mu C} = 12\; {\rm (\mu C)^(2)}`.

Thus, the product of the magnitude of the two charges has been scaled to
`12\; {\rm \mu C}` from
`21\; {\rm \mu C}` . The magnitude of the electrostatic force between the two charges would be scaled from
`25\; {\rm N}` to
`25\; {\rm N} * (12 / 21) \approx 14\; {\rm N}`.