# Tension in a rope connecting charged spheres.

1. Mar 13, 2012

### -Dragoon-

1. The problem statement, all variables and given/known data
Two positive charged spheres, with masses m = 2.0 g and with the same charge 2 µC are connected by a rope that is a distance of 5 cm. The charged spheres are at rest and the system is in static equilibrium.

2. Relevant equations

N/A.

3. The attempt at a solution
The system is in static equilibrium, which implies the net force is 0:
$\displaystyle\sum_i (f_x)_i = F_1on2 - F_2on1 + T = 0 => T = F_2on1 - F_1on2 = \frac{kq^2}{r^2} - \frac{kq^2}{r^2} = 0.$

Thus, I end up with tension being equal to zero since the force the charged sphere on the left exerts on the charged sphere on the right is equal and opposite to the forced the charged sphere on the right exerts on the left.

But, I have the wrong answer. Where did I go wrong?

2. Mar 13, 2012

### Staff: Mentor

Tension acts on both spheres, and in opposite directions. If you sum all the forces you'll end up with the unsurprising result that |F2on1| = |F1on2|, that is, they are both pushing each other with the same magnitude of force.

To find the tension, isolate one of the spheres and draw the Free Body Diagram. Sum the forces there. What should they sum to for static equilibrium?