Suppose you touched a pith ball suspended from an insulating string to a charged

Question

Suppose you touched a pith ball suspended from an insulating string to a charged Teflon rod. You then made a second pith ball touch the first one with no other objects near by. You then put the top of the strings next to each other as shown at right. The two pith balls would be separated by 2 cm. The mass of each pith ball is 0.1 g and the length of each of the string is 20 cm. (ignore the mass of the strings)

The goal is to determine the magnitude of the charge on each ball. We will accomplish this by first determining the electric force that each ball exerts on the other.

Draw free body diagrams for the two balls.

Explanation / Answer

If ? is the semi vertical angle between the strings F tan ? = mg where F is the electrostatic force on one of the charges F = kq^2 /r^2 where r is the distance between the charges. kq1^2 /r^2 tan ? = mg ---------for the first experiment kq2^2 /r^2 tan (2?) = mg ---------for the second experiment Divinding one by the other (q1/q2)^2 * tan ? / tan (2?) = 1 (q1/q2) = ? [tan (2?) / tan ?] = ============================= tan ? = 1/ (20^2-1) = 0.0025 Since ? is small tan 2 ? = 2 tan ? ? [tan (2?) / tan ?] = ?2 = 1.414 (q1/q2) = 1.414

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