2 small spheres each of mass m and charge q, lie inside a nonconducting smooth hemisphere of radius R. (1) Find q if the equilibrium separation between the charges is d (2) Compute the potential energy in this configuration.
2006-12-13 02:30:00 · 2 answers · asked by saudipta c 5 in Science & Mathematics ➔ Physics
You need to balance the force of gravity down the slope against the repelling electrostatic force up the slope. Where these forces are equal and opposite will be a spot where the slope make an angle theta with the horizontal. (e is the electric constant)
Force due to grav = mg sin theta
Force due to ES force =
q^2 cos theta
-----------------
4*pi*e*d^2
Using trig, you can find that 0.5*d = R sin theta
From that, theta = arcsin (d/2R)
Balancing equations, you can find that:
q^2 cos theta = 16*pi*e*mg*R^2*(sin theta)^3
divide by cos theta on both sides and sub in for theta:
q^2 = 16*pi*e*mg*R^2*(d/2R)^3 / sqrt (1-(d/2R)^2)
q = sqrt of the above
Potential energy should be zero because they are in equilibrium. If they were further apart, gravity would bring them closer together, and if they were closer together, ES repulsion would force them back up the slope.
2006-12-13 06:20:55 · answer #1 · answered by Minnesota_Slinger 3 · 1⤊ 0⤋
u have to substitute in the below formula
charge=q1q2/r^2
2006-12-13 10:05:30 · answer #2 · answered by Aditya N 2 · 1⤊ 0⤋