When conducting objects (such as metals) are connected for a brief time, charge

Question

When conducting objects (such as metals) are connected for a brief time, charge can be made to flow quite
easily from one to the other, even if the objects are in contact for an extremely brief amount of time. To that
end, consider two identical metallic ball-bearings (i.e., two very tiny metallic solid spheres) having unknown
charges q1 and q2. It is found that when they are placed 1 m apart, they experience a 25-N attractive force.
(a) What can you conclude about the charges on these metal marbles from the information given?
(b) The ball-bearings are made to touch very briefly and then are separated by 1 m again. What can you
conclude about the charges now? Explain.
(c) Suppose that when the charges are 1 m apart, after briefly touching, they again feel a force of 25 N.
Determine the charges q1 and q2.

Explanation / Answer

As force is attarctive the chargs q1 and q2 are of opposite sign

F = kq1q2/1 = 25 N

a) q1 q2 = 25/9.0e-9 = -2.78 e-9 C2

b) When they touch each other total charge (q1+q2) is ditributed across the two spheres equally as they have the same capacity

if q is the charge on each aftre seperation

2q = q1 + q2

c) when they are 1 m apart after seperation

Force between them

F = kq2/1 = 25 N ( Thsi time it is repulsive as both are of same sign

q2 = 2.79e-9

q = +/- 5.27e-5 C

q1 + q2 = 2q = 10.54 e-5 ( we take the absolute value)

(q1-q2)2   = (q1 + q2 )2 - 4q1q2

q1 -q2    = 1.49 e-4

q1 + q2 = 1.054e-4

solving the above we get

q1 = 1.27e-4

q2 = -0.22e-4 C

The signs of q1 and q2 may be interchanged, oneof them is +ve while the other is -ve. both shall be of opposite sign.

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