A Faraday ice pail similar to the one you used in lab is shown to the right. As

Question

A Faraday ice pail similar to the one you used in lab is shown to the right. As you recall, the principle of its operation relies on the proportionality between the charge on the inner pail and the potential difference between the inner pail and the ground. Suppose the relationship between charge q and potential difference V is given by V=2.5E16 q. When a charged wand is inserted into the inner pail and touches it, the electrometer reading is -18.0 volts. (a) How much charge resided on the wand? (b) Before grounding the pail, a second wand is inserted into the ice pail and touches it. The electrometer reading is now +30.0 volts. How much charge resided in the second wand? (c) If the two wands were separated by 4.0 cm before they were discharged onto the ice pail, what force did either exert on the other? (d) Was it attractive of repulsive? Assume that no leakage of charge occurs during the experiment - all charge on the wand is transferred to the ice pail when it touches the ice pail. Recall that (1/4pi e0)=9E9 Nm2/C2.

The pail looks kind of like this: http://tinyurl.com/6g4g3sv

The answers given by my TA are (a) -7.2E-16C (b) 1.92E-15C (c) -7.77E-18N (d) attractive

Explanation / Answer

(a) V = - 18 volts 2.5 x 10^16 q1 = - 18 volts q1 = - 7.2 x 10^-16 C (b) V =  30 volts 2.5 x 10^16 ( q1 + q2 ) = 30 volts q1 + q2 = 1.2 x 10^-15 C q2 = 1.2 x 10^-15 - ( - 7.2 x 10^-16 )      = 1.2 x 10^-15 + 0.72 x 10^-15      = 1.92 x 10^-15 C (c) F = k q1 q2 / r^2    = 9 x 10^9 * 7.2 x 10^-16 * -1.92 x 10^-15 / ( 4 x 10^-2)^2    = - 7.77 x 10^-18 N (d) As q1 and q2 are opposite, the force between them is attractive. V =  30 volts 2.5 x 10^16 ( q1 + q2 ) = 30 volts q1 + q2 = 1.2 x 10^-15 C q2 = 1.2 x 10^-15 - ( - 7.2 x 10^-16 )      = 1.2 x 10^-15 + 0.72 x 10^-15      = 1.92 x 10^-15 C (c) F = k q1 q2 / r^2    = 9 x 10^9 * 7.2 x 10^-16 * -1.92 x 10^-15 / ( 4 x 10^-2)^2    = - 7.77 x 10^-18 N (d) As q1 and q2 are opposite, the force between them is attractive.

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