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A faraday ice pail similar to the one you will use is shown to the right. 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 ground. suppose the relationship between charge q and potential difference V is given by q=V 3.50x10^-14. when a blue wand and a white wand are inserted into the ice pail at the same time without the wands touching, the electrometer reading was +75.8 volts. when only the white wand was removed, the electrometer reading changed to -23.0 volts.
a. How much charge resides on the blue wand?
b. how much charge resides on the white wand?
c. when the two wands are held 3.25cm apart, what is the magnitude of the force exerted on either wand, assuming each wand is considered a point charge?
d. if the charge of one electron is -1.60x10^-19C, how many electrons are on the blue wand? assume no leakage of charge

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boffeemadrid

Answer:

[tex]-8.05\times 10^{-13}\ C[/tex]

[tex]3.458\times 10^{-12}\ C[/tex]

[tex]2.3692660923\times 10^{-11}\ N[/tex]

5031250

Explanation:

V = Voltage

C = Capacitance = [tex]3.5\times 10^{-14}\ F[/tex]

r = Distance = 3.25 cm

Charge is given by

[tex]q=VC\\\Rightarrow q=3.5\times 10^{-14}\times -23\\\Rightarrow q=-8.05\times 10^{-13}\ C[/tex]

The charge on the blue wand is [tex]-8.05\times 10^{-13}\ C[/tex]

[tex]q=(75.8-(-23))\times 3.5\times 10^{-14}\\\Rightarrow q=3.458\times 10^{-12}\ C[/tex]

The charge on the white wand is [tex]3.458\times 10^{-12}\ C[/tex]

Electrical force is given by

[tex]F=\dfrac{kq_1q_2}{r^2}\\\Rightarrow F=\dfrac{8.99\times 10^9\times -8.05\times 10^{-13}\times 3.458\times 10^{-12}}{0.0325^2}\\\Rightarrow F=-2.3692660923\times 10^{-11}\ N[/tex]

The magnitude of force is [tex]2.3692660923\times 10^{-11}\ N[/tex]

Number of electrons is given by

[tex]n=\dfrac{-8.05\times 10^{-13}}{-1.6\times 10^{-19}}=\\\Rightarrow n=5031250[/tex]

The number of electrons in the blue wand is 5031250

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