Question

What must the center-to-center distance between two point charges of 60.0 nC be to have a force of 4 N between them?

Answer 1

Given:

• Each Charge = 60.0 nC

,

• Force between the charges = 4 N

Let's find the center-to-center distance between thw two point charges.

To find the center-to-center distance, apply the formula:

`F=\frac{kQ_1Q_2_{}}{r^2}`

Where:

Q1 = Q2 = 60.0 nC

k is the Coulomb's constant = 9 x 10⁹ N⋅m^2⋅C^-2

r is the distance

F is the force = 4 N

Rewrite the formula for r, input the values and solve for r.

We have:

`\begin{gathered} r=\sqrt[]{(kQ_1Q_2)/(F)} \\ \\ r=\sqrt{(9*10^9*(60*10^(-9))*(60*10^(-9)))/(4)} \\ \\ r=\sqrt[]{8.1*10^(-6)} \\ \\ r=2.8*10^(-3)\text{ m }\approx2.8mm \end{gathered}`

Therefore, the center-to-center distance is 2.8 mm

ANSWER:

2.8 mm