A thin circular sheet of glass of diameter 7 meters is rubbed with a cloth on on

Question

A thin circular sheet of glass of diameter 7 meters is rubbed with a cloth on one surface, and becomes charged uniformly. A chloride ion (a chlorine atom which has gained one extra electron) passes near the glass sheet. When the chloride ion is near the center of the sheet, at a location 0.7 mm from the sheet, it experiences an electric force of 4e-15 N, toward the glass sheet. In this problem, use the value e0 = 8.85e-12 C2/(N·m2)
It will be useful to you to draw a diagram on paper, showing field vectors, force vectors, and charges, before answering the following questions about this situation.

How much charge is on the surface of the glass disk? (give amount, including sign, and correct units)

Explanation / Answer

This is effectively an infinite sheet of charge, since the disk is 7 meters in diameter and the field point is 0.7 mm away. Thus the field E = /20. We also know F = qE and we are given F and q; so

E = F/q = (4 * 10-15 N)/(1.602 * 10-19 C) = 2.50 * 104 N/C

therefore

= 20E = (2 * 8.854 * 10-12 C2/Nm2)(2.50 * 104 N/C) = 4.42 * 10-7 C/m2

Since the area of the disk is (3.5 m)2 = 38.4845 m2, the total charge is the product of that times , or 1.70 * 10-5 C, and it is positive.

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