Two insulating spheres are charged to the same charge. One is screwed into the g

Question

Two insulating spheres are charged to the same charge. One is screwed into the ground.

If each sphere is 0.25 kg, how much charge do you need to give each sphere to achieve 1 m of levitation? Draw a free-body diagram.

If you use two parallel plates instead w/ 500 V between them and the plate w/ higher potential on the bottom and give the ball 2.5 mC of charge, what should the plate separation be so that the sphere levitates and stays in place? Include a FB diagram.

If you were to increase the potential difference between the plates, what would happen?

Explanation / Answer

For the first condition to occur,

F(electric) = F(gravity)

kq^2/r^2 = mg

q = sqrt (m g r^2/k)

q = sqrt (0.25 x 9.8 x 1^2/9 x 10^9) = 1.65 x 10^-5 C

Hence, q = 1.65 x 10^-5 C = 16.5 micro C

# for this condition to happen,

PE(gravity) = U(stored)

mg R = 1/2 C V^2

R = 0.5 C V^2/mg

C = Q/V = 2.5 x 10^-3/500 = 5 x 10^-6

R = 0.25 x 5 x 10^-6 x 500^2/0.25 x 9.8 = 0.128 m

Hence, R = 0.128 m

If we increase the V, the distance will also increase, as it is directly proportional to the square of distance.

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