Download Exam 2 Physics 195B (3/14/02)

Physics 196 Fall 2012
Exam 4
Permeability of free space
Mass of Proton
Avogadro’s number
Bohr Magneton
Name:
μ0 = 4π×10-7 T-m/A
mp=1.67×10-27 kg
NA=6.02×1023
μB = 9.27×10-24 J/T
PART 1 ( 52 points total. 4 points each.)
Circle the correct answer for the next 13 questions
1. A 5.0mm short wire at the origin of a right hand rectangular coordinate system (x,y,z) carries a current of
2.0A in the direction of the x-axis. Find the magnetic field it creates at the point that has the coordinates
(2, 1, 2) in meters.
(a) (-7.4 ĵ + 3.7k̂)´10-11 (T )
(b)
(c)
(d)
2. A current-carrying circular loop of radius 5.0cm as shown creates a magnetic field
of 8.0T at the center pointing out of the paper. The magnitude and direction of
the current is
(a)
(b) 0.64A counter - clockwise
(c)
(d)
3. Refer to the diagram showing a square wire frame abcd carrying a clockwise current in a uniform magnetic
field directed to the left. Draw in the torque vector and indicate the direction of motion of the point a as a
result of the torque, assuming the frame starts at rest.
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4. A 4.0A current runs downward in a very long wire. What is the magnetic field at the point
indicated that is 3.0cm from the wire?
(a) 27mT into paper
(b) 0.4mT out of paper
(c) 0.8mT into paper
(d) 0.8mT out of paper
5. The diagram shows two infinitely long wires at the opposite corners of a square carrying equal currents into
and out of the paper respectively. Draw the direction of the magnetic field they create at one of the
unoccupied corner d of the square.
6. The magnetic field inside a 10-cm long solenoid is 25.0mT when the current is 5.0A. Assuming the
approximation of an infinitely long solenoid applies, the number of windings is closest to
(a)
(b)
(c)
(d)
400
500
600
700
7. The diagram shows two horizontal thin rods parallel to each other. The bottom is
fixed but the top rod is free to move up and down. When they carry oppositely
directed currents of 3.0A, the rod on top is found to be levitated 2.0mm above the
other. What is the separation between the rods if both currents are increased to 9.0A?
(a) 3.5 mm
(b)
(c)
(d)
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8. The diagram shows several infinitely long wires carrying currents of magnitudes and directions indicated.
Draw a closed loop so that the circulation integral ò B × d = 3m0 I . Indicate the direction of taking the
integral.
9. A very long rod in the shape of a circular cylinder of radius R carries a current I in the
direction of its axis. The current is uniformly distributed throughout its cross-section.
Find the magnetic field at a point inside the rod that is at a distance of 3R / 4 from the
axis.
(a)
(b)
(c)
(d)
3m0 I
3m0 I
3m0 I
3m0 I
8p R
8p R
8p R
8p R
10. The unit of magnetization is
(a) A / m
(b)
(c)
(d)
11. A sample of a certain metal is placed inside a solenoid carrying a current in the
indicated direction. As a result, an induced magnetic field is produced in the
metal in the direction shown. It can be concluded that the metal is
(a) diamagnetic
(b) paramagnetic
(c) ferromagnetic
(d) none of the above
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12. The magnetic flux through a coil rotating in a magnetic field is given by the equation fm = 2.0cos (p t ) Wb
The induced emf in the coil at t = 0.4s is
(a) 7.47 V
(b)
(c)
(d)
13. Indicate the direction of the induced current in a wire frame being pulled out of a region where the magnetic
field is pointing into the paper.
PART B (48 points)
1. (12 pts) Refer to the diagram showing two infinitely long currentcarrying wires parallel to the z-axis. The positions and the currents are
indicated. Find
(a) (6 pts) the magnitude and direction of the magnetic field at the
point P where x = a and the point Q where x = -a on the x-axis.
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(b) ( 3 pts) the x coordinate of a point on the x-axis where the magnetic field is zero.
(c) (3 pts) A straight segment of a wire is placed on
the x-axis, where it occupies the interval
between the points x = 3a and x = 4a . The wire
carries a current I running in the x-direction.
Find the magnitude and direction of the force
on the segment due to the magnetic field of the
two infinitely long wires.
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2. (12 pts) A square wire frame abcd with dimensions 20cm ´ 20cm rests on the
x-y plane, carrying a clockwise current of 3.0A when viewed from a location
on the positive half of the z-axis. A 1.5T magnetic field exists in the region
pointing in the x-direction.
(a) (6 points) Use the ijˆ k̂ notation to write the magnetic moment vector
and the torque vector
(b) (3 points) Indicate the direction of motion of the corners of the square as a result of the torque,
assuming the frame is initially at rest
(c) (3 points) Find the minimum amount of work to turn the frame
through 60 about the y-axis in the direction shown.
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3. (12 pts) A circular wire loop of radius 0.35m and electrical resistance 50.0
is placed in a region where there is a uniform magnetic field perpendicular to
the plane of the loop.
(a) (4 points) At the beginning, the magnetic field is pointing out of the paper
and equal to 2.0T. During the next 6.0s, the magnetic field increases to
4.0T. Find the magnitude and direction of the average induced emf and
induced current during this time.
(b) After the magnetic field has reached 4.0T, it stays constant. The loop starts to rotate about a diameter
with a period of 8.0s. Find
(1) (4 points) the average induced emf during the first 4.0s of turn
(2) (4 points) the peak emf attained in the course of the rotation
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4. (12 pts) A perfectly conducting rod of length L = 0.4m and mass
m = 2.0kg lies on a pair of smooth railings connected to a 50.0 resistor.
The whole assembly is in a uniform magnetic field B =1.2T pointing into
the paper. At t = 0 , the rod is found to be moving with velocity 9.0m / s
to the right.
(a) (3 points) Find the magnitude and direction of the induced current at t = 0 .
(b) (3 points) Find the magnitude and direction of the force on the rod at t = 0 .
(c) (3 points) Find the time when the velocity of the rod drops to 6.0m / s
(d) (3 points) Find the total energy delivered to the resistor if the rod is allowed to continually slow
down.
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