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MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
8.02
Spring
2010
8.02 Exam One Solutions Spring 2010
Problem 1 (25 points)
Question 1 (5 points)
1.
Above we show the grass seeds representation of the field of four point charges,
located at the positions indicated by the numbers.
Which statement is true about the signs
of these charges:
a)
All four charges have the same sign.
b)
Charges 1 and 2 have the same sign, and that sign is opposite the sign of
3 and 4.
c)
Charges 1 and 3 have the same sign, and that sign is opposite the sign of
2 and 4.
d)
Charges 1 and 4 have the same sign, and that sign is opposite the sign of
2 and 3.
e)
None of the above.
Solution b.
Field lines continuously connect charges 1 and 3, and 2 and 4 respectively,
indicating that the charge of those pairs are opposite in sign. The field is a zero between
charges 1 and 2 indicating that they repel and hence are of the same sign. A smilar
argument holds for charges 3 and 4.

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Question 2 (5 points)
The grass seeds figure below shows the electric field of three charges with charges +1,
+1, and -1,
The Gaussian surface in the figure is a sphere containing two of the charges.
The total electric flux through the spherical Gaussian surface is
a)
Positive
b)
Negative
c)
Zero
d)
Impossible to determine without more information
Solution c.
Because the field lines connect the two charges within the Gaussian surface
they must have opposite sign. Therefore the charge enclosed in the Gaussian surface is
zero. Hence the electric flux through the surface of the Gaussian surface is also zero.