Physics 2Ba quiz 3 solutions
(Dated: January 31, 2009
2:31)
Problem 1
Electric field lines go from region A to region B. We must conclude that
A) The electric potential in region A is positive while the electric potential in region B is negative
B) The electric potential in region B is positive while the electric potential in region A is negative
C) The electric potential is everywhere positive and larger in region A than in region B
D) The electric potential is everywhere positive and larger in region B than in region A
E) None of the above
The correct answer is
E
. The change in potential, Δ
V
is given by the following formula.
Δ
V
=

Z
B
A
E
·
d
r
(1)
Since the electric field lines point from
B
to
A
, if we choose a straight integration path between the two points, then
the dot product
E
·
d
r
is positive since the electric field points from
A
to
B
(cos
θ
= 1). The integral will always be
positive and so we must conclude from Eq. (1) that Δ
V
is negative. However, we only know the change in potential
from
A
to
B
, we
do not
know the absolute potential. There is not enough information, since in order to determine
whether the potential is positive or negative, we must be told something about the absolute potential at
A
or
B
.
Problem 2
The figure below shows equipotentials surrounding a pair of charges
Q
A
and
Q
B
. The value of the potential
halfway between the charges is indicated. Which of the statements below applies to the charges?
The correct answer is
A
. The symmetry of the diagram tell us that the charges must have equal magnitude. If the
charges had the same sign, the potential would not be zero anywhere except possibly at
r
=
∞
. The fact that there
exists an equipotential line with
V
= 0, we know that along this line the contribution from each charge must cancel
against each other; therefore, the charges have opposite sign. Also, any point on the
V
= 0 line has the same
distance to each charge, and so again we are forced to conclude the charges have equal magnitude.
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 Winter '08
 schuller
 Electric Potential, Energy, Force, Potential Energy, Correct Answer, Electric charge, Wnc

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