A ball, which we can treat as a point charge, has a charge of +Q and a weight of

Question

A ball, which we can treat as a point charge, has a charge of +Q and a weight of 9.00 N. This ball is 50 cm away from a ball of charge -10Q, which is fixed in position. The +Q ball is 30 cm vertically below, and 40 cm horizontally, from the other ball, and the +Q ball is held in equilibrium at that position by a string which happens to be perfectly horizontal. Note that you should be able to do parts (a) and (b), at least, without a calculator. HINT: Draw a free-body diagram.


(a) What is the magnitude of the electrostatic force that the ball with the charge of -10Q exerts on the ball with the charge of +Q?


N

(b) What is the magnitude of the tension in the string?


N

(c) What is the value of Q?
C

Explanation / Answer

The magnitude of the electrostatic force that the ball with the charge of -10Q exerts on the ball with the charge of +Q = Kq1q2/r2 = 9 X 109 X Q X 10Q /0.25 = 36Q2 X1010

Vertical component of this force = 9N

Hence 36Q2 X1010 X 3/5 = 9

This gives Q = 6.45C

magnitude of the electrostatic force = 36Q2 X1010 = 15N

Tension in the string = 15 X 4/5 = 12N

(a) 15N

(b)12N

(c)6.45 X 10-6C

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