Consider the following figure
Each red point is a particle of a known mass that carries charge Q/2 and connected to a the box by a thread of known length. This problem can be solved easily to find Q
How would one handle the situation, had the two branches been leaves of an electroscope of equal known masses instead of point particles? (now every leaf is charged continuously) Is this problem solvable?
[In this new situation the left branch is carrying same total charge as the right one by symmetry. But to analyse the problem for static equilibrium for the left branch say, I tried to identify the forces on the left branch:
- there will be the weight of the branch acting at the center of mass (at a distance 35 cm) points down.
- an electrostatic force (which is not uniform?) acting on the whole branch because of the
electric field (which is not uniform?) due to the right branch
- the force on the leave at the connection point with the red box (how to find it?)]
Is it possible to find the total charge/charge density on every branch?