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HW8
Due: 11:00pm on Thursday, April 15, 2010
Note:
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Charged Aluminum Spheres
Description:
Find the number of electrons in an aluminum sphere. Calculate the number of electrons that must be removed from one sphere and added to another to create a given attractive force, and find the
fraction of electrons per sphere this number represents.
Two small aluminum spheres, each of mass 0.0250 kilograms, are separated by 80.0 centimeters.
Part A
How many electrons does each sphere contain? (The atomic mass of aluminum is 26.982 grams per mole, and its atomic number is 13.)
Hint A.1
The definition of mole and atomic number
In one mole (
) of any material, there are approximately
atoms present. The number of atoms per mole is called
Avogadro's number
. The atomic number of an element is the number of
protons (and therefore also the number of electrons) in an atom of that element.
Hint A.2
How many electrons per mole of aluminum?
How many electrons are there in a mole of aluminum?
Express your answer numerically.
ANSWER:
Hint A.3
How many electrons per kilogram of aluminum?
How many electrons are in a kilogram of aluminum?
Express your answer numerically.
ANSWER:
Express your answer numerically.
ANSWER:
Part B
How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude
(roughly one ton)? Assume that the spheres
may be treated as point charges.
Hint B.1
How to approach the problem
Use Coulomb's law to find the charge needed to produce the given force. Then use the charge of an electron to determine the number of electrons necessary to produce the calculated charge.
Hint B.2
Find the relationship between the charges of the spheres
Assume that after some electrons have been removed from it, the first sphere ends up with a net charge of
. What would be the charge on the other sphere,
, after these extra electrons are added to it?
Express your answer in terms of
and any necessary constants.
ANSWER:
=
Express your answer numerically.
ANSWER:
Part C
What fraction of all the electrons in one of the spheres does this represent?
Express your answer numerically.
ANSWER:
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Coulomb's Law Tutorial
Description:
Use Coulomb's law to compute the (vector) force between two, and subsequently multiple, electric charges (both positive and negative). One charge acts at an angle of pi/4 radians relative to the
given coordinate axes, and thus trigonometry is required to solve the problem.
Learning Goal:
To understand how to calculate forces between charged particles, particularly the dependence on the sign of the charges and the distance between them.
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 Fall '10
 MichaelChen
 Physics, Charge, Electric charge

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