electricity?

Question

If the electrical force of repulsion between two 1 C charges is 10 N, how far apart are they?

Answer 1

The force exerted on a charged object by another charged object is given by,
F = k_e * q * Q / r^2
Where k_e is the Coulomb constant, q and Q are the respective charges on the objects, and r is the distance in between the objects.

You are given the values for q and Q, and it is assumed you know the value for k_e (= 8.99 E9 N (m/C)^2). You are also given the value for the force exerted on the objects, so you have everything you need to solve for the one unknown, r.

Rearranging the above equation to solve for r, we get,
r^2 = k_e * q * Q / F
r = sqrt (k_e * q * Q / F)

r = sqrt((8.99 E9 N m^2 / C^2) * (1 C) * (1 C) / (10 N))
r = sqrt (8.99 E8 m^2)
r = 29983 meters

So the distance in between the two objects is about 30 km.