PHY2054 Spring 2007
1
Prof. Eugene Dunnam
Prof. Paul Avery
Apr. 28, 2007
Exam 4 Solutions
1. A charge of
−
5 microC is placed at the origin and a +10 microC charge is located at x =
−
1.0
m.
Where, on the x-axis, is the net electrostatic field equal to zero, and is the electrostatic poten-
tial at this point also zero?
(1)
x
= +2.41 m; no
(2)
x
=
−
2.41 m; no
(3)
x
= +1.00 m; yes
(4)
x
=
−
0.62 m; no
(5) none of these
The electric field must be zero for points to the right of the smaller charge (x > 0) because in
that region the field from the larger charge is compensated by the greater distance.
If +2q is the
charge at x =
−
1.0 and
−
q is the charge at the origin, then the equation for E
x
= 0 can be written
(
)
2
2
/
2
/
1
0
kq
x
kq
x
−
+
+
=
.
Solving yields
2
1
2.41
x
=
+
+
±
m.
2. The sketch depicts a 50-turn rectangular loop of dimensions
a
= 55 cm and
b
= 130 cm, and
rotated by an angle
θ
= 65
°
from the
y
axis. It is hinged along the
z
axis and immersed in a uni-
form magnetic field B = 0.27 T pointing in the +
z
direction. The current in the loop is 4.5 A. The
torque on the loop (in N
⋅
m) and its direction of rotation, viewed from above, is (CW = clockwise
and CCW = counterclockwise)
(1) 0.0
(2) 0.79, CW
(3) 0.37, CCW
(4) 0.87, CW
(5) 2.92, CCW
Only the currents along the top and bottom of the loop contribute to the torque since the currents
on the side generate zero force apiece.
However, the torques from the top and bottom parts of
the loop cancel because the forces are equal and opposite and the lever arm is the same.
x
z
y
±
a
b
B

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