Question

by what factor will the electrostatic force between two charged particles change if you: multiply one charge by 5.4, multiply the other charge by 4.6, and multiply the distance between them by 3.2?

Answer 1

The electrostatic force between the two would increase to approximately
`2.4` times the initial value.

Step-by-step explanation:

By Coulomb's Law, the magnitude of the electrostatic force between two point charges is:

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

Where:

• 
  `k` is a constant (Coulomb's Constant),
• 
  `q_(1)` and
  `q_(2)` are the magnitudes of the charge on the two point charges, and
• 
  `r` is the distance between the two point charges.

In this question,
`q_(1)` becomes
`(5.4\, q_(1))`,
`q_(2)` becomes
`(4.6\, q_(2))`, and
`r` becomes
`(3.2\, r)`. Thus, the magnitude of the electrostatic force between the two charges would become:

`\begin{aligned} & (k\, (5.4\, q_(1))\, (4.6\, q_(2)))/((3.2\, r)^(2)) \\ =\; & ((5.4)\, (4.6))/((3.2)^(2))\, \left((k\, q_(1)\, q_(2))/(r^(2))\right) \\ \approx \; & 2.4\, \left((k\, q_(1)\, q_(2))/(r^(2))\right)\end{aligned}`.

In other words, the magnitude of the electrostatic force between the two charges would become approximately
`2.4` times the initial value.