You break a piece of Styrofoam packing material, and it releases lots of little spheres whose electric charge makes them stick annoyingly to you.

If two of the spheres carry equal charges and repel with a force of 21 mN when they're 15 mm apart, what's the magnitude of the charge on each?

2.24*10⁻⁸ C

Explanation:

From coulomb's law,

F = kq1q2/r² ... Equation 1

Where F = Repulsive force between the two charges, q1 = charge on the first sphere, q2 = charge on the second sphere, r = distance between the sphere, k = proportionality constant.

Note: q1 = q2 = q,

Then, we can rewrite equation 1 as,

F = kq²/r²

making q the subject of the equation

q = √ (Fr²/k) ... Equation 2

Given: F = 21 mN = 0.021 N, r = 15 mm = 0.015 m

Constant: k = 9.0*10⁹ Nm²/C²

Substituting these values into equation 2

q = √ (0.021*0.015²/9.0*10⁹)

q = √ (5*10⁻¹⁶)

q = 2.24*10⁻⁸ C.

Hence the charge on each sphere = 2.24*10⁻⁸ C