How much charge was placed on each sphere?

Question

Two .20g metal spheres are hung from a common point by nonconducting threads 30cm long. both are given identical charges, and the eectrostatic repulsion forces them apart until the angle between the threads is 20 degrees. how much charge was placed on each sphere?

ok how would i start this problem?? can u even do this without knowing the charges? id really appreaciate some help on this stuff, i dont get it. thanks

Answer 1

First figure out the force required to hold the spheres at a 20 degree angle, actually 10 degrees for each sphere, based on g(9.8nm/s^2) the mass of the spheres and the length of the string. Then you can use coulombs law to calculate the charge on each sphere, in this case Q1=Q2 so you can just use Q1 squared.

Answer 2

this is a problem in balancing forces.

Calculate the side force to push your sphere to this angle under the influences of gravity.

Then you calculate the repulsion between 2 objects of like charge as a function of that charge...

Then you solve for the known force.

Answer 3

Draw yourself a force diagram on a sphere with the tension and the gravity and the electrostatic repulsion. If you draw it right, you should see that:
tangent (angle/2) = yforce / xforce

yforce = weight = mg

xforce = electrostatic repulsion = kq^2 / r^2

The distance between the spheres can be expressed in terms of the angle and the length of the string:
r = 2 l sin (angle/2)

Put it all together

tan (theta/2) = 4mg l^2 sin^2 (theta/2) / kq^2

Do some algabra to solve for charge: q =
sqrt(4mg l^2 sin^2 (theta/2) / (k tan (theta/2)))

They give you m, l, and theta. You know g. Look up k. Plugnchug.