Physics 112 HW19
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Due Monday, 3 November 2014
µ06. The triangular loop of wire shown in the diagram at right carries
Q
a current of 5.00 A in the direction shown. The loop is in a uniform
B
magnetic field that has magnitude B = 3.00 T and the same direction
0.600 m
as the current inside PQ of the loop.
I
I
I
a) Find the force exerted by the magnetic field on each side of the
P
triangle. If the force is not zero, specify its direction.
0.800 m
b) What is the net force on the loop?
c) The loop is pivoted about an axis that lies along side PR. Use
the forces calculated in part (a) to calculate the torque on each side of the loop about this
axis.
d) What is the magnitude of the net torque on this loop? Calculate it using two methods:
IABsinθ and by summing your answers from part (c). Describe the “sense” of the torque
(what direction it twists the loop around).
BI01. Positive point charges q1 = 8.00 μC and q2 = 3.00 μC are moving relative to an observer
at point P as shown in the diagram at right. The distance d is
q1
v1
0.120 m. q1 has velocity v1 of 4,500,000 m/s to the right and q2
has velocity v2 of 9,000,000 m/s to the left.
d
a) When the two charges are at the locations shown in the
P
figure, what are the magnitude and direction of the net
d
magnetic field they produce at point P?
b) What are the magnetic forces (magnitude and direction)
q2
v2
the charges exert on each other when they are at the
locations shown in the diagram?
c) (OPTIONAL) If the direction of q2’s velocity were reversed so that both charges were
moving in the same direction, what are the magnetic forces (magnitude and direction) the
charges exert on each other when they are at the locations shown in the diagram?
d) (OPTIONAL) Now make q2 go in its original direction, but make q2 = –3.00 μC.
Calculate the net magnetic field at point P and the magnetic forces the charges exert on
each other in this case.
BI02. The figure at right shows two point charges qa and qb
moving as shown.
a) When the charges are at the positions shown, find the
magnitude and direction of the net magnetic field at
the origin.
b) Find the magnetic force one exerts on the other.
y
q1 = 8.00 μC
v1 = 90,000 m/s
0.300 m
v2 = 65,000 m/s
x
q2 = – 5.00 μC
O
0.400 m
(over)
R
ILB03. Two long, parallel wires are separated by a distance of 0.400 m. Their currents, I1 =
5.00 A and I2 = 2.00 A, are anti-parallel (they go in opposite directions).
a) Calculate the magnitude of the force exerted by each wire on a 1.20 m length of the
other. Is the force attractive or repulsive?
b) Each current is doubled, so that I1 becomes 10.00 A and I2 becomes 4.00 A. Now what
is the magnitude of the force that each wire exerts on a 1.20-m length of the other?
BI03. A long, straight wire lies along the z-axis and carries a 4.00 A current in the +zdirection. Find the magnetic field (magnitude and direction) produced at the following points
by a 0.500mm segment of the wire centered at the origin: a) x = 2.00 m, y = 0, z = 0; b) x
= 0, y = 2.00 m, z = 0; c) x = 2.00 m, y = 2.00 m, z = 0; d) x = 0, y = 0, z = 2.00 m.
BI04. Two long, straight, parallel wires 10.0 cm apart carry equal 4.00 A
currents in the same direction. Using the equation for the magnetic field
due to an infinite line, find the magnitude and direction of the magnetic
field
a) at point P1 midway between the wires,
b) at point P2 which is 25.0 cm to the right of point P1, and
c) at point P3 which is 20.0 cm directly above point P1.
BI05. Calculate the magnitude and direction of the magnetic field
at point P in the figure at right in terms of R and I.
P1
10.0 cm
I
R
P
BI06. The figure at right shows an end view of two
long, parallel wires perpendicular to the xy plane,
each carrying current I, but in opposite directions.
a) Copy the diagram, and draw vectors to show
the B field of each wire and the net B field
at point P.
b) Derive the expression for the magnitude of
B at any point on the x-axis in terms of the
x-coordinate of the point, a, I, and
fundamental constants.
(over)
y
I
a
P
x
a
 I
x