Physics 196 Spring 2013
Exam 4
Name:
Permeability of free space
Mass of Proton
Avogadro’s number
Bohr Magneton
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 ( 48 points total. 4 points each.)
Circle the correct answer for the next 12 questions
1. A 3.0mm short wire at the origin of a right hand rectangular coordinate system (x,y,z) carries a current of
9.0A running in the negative x-direction. Find the magnetic field it creates at the point (2,-1,2) where
coordinates are measured in meters.
(a) (4.0 ĵ - 2.0k̂)´10-10 (T )
(b) (4.0 ĵ + 2.0k̂)´10-10 (T )
(c) (2.0 ĵ - k̂)´10-10 (T )
(d) (2.0 ĵ + k̂)´10-10 (T )
2. The diagram shows a very long current-carrying wire producing a
80mT magnetic field at a point 3.0mm away pointing into of the paper. The
current in the wire is
(a) 2.4A
(b) 2.4A
(c) 1.2A
(d) 1.2A
up
down
up
down
3. A 15cm long solenoid carrying 4.0A current produces a magnetic field of 100mT in its interior. Find the
number of turns in the solenoid assuming it can be considered to be infinitely long. (Choose the closest
answer)
(a) 1000
(b) 2000
(c) 3000
(d) 4000
1
4. The diagram shows an infinitely long wire and a circular loop on
the same plane both carrying currents. The current in the loop is
I , and runs clockwise. What is the current in the straight wire if
the magnetic field at the center of the loop is zero?
(a)
(b)
(c)
(d)
4.7I,
4.7I,
2.6I,
2.6I,
to the right
to the left
to the right
to the left
5. The diagram shows three very long wires A,B and C forming an isosceles triangle with AC=BC. They carry
currents of the same magnitude in the directions indicated. Draw a vector on C to indicate the direction of
the force on it due to the magnetic field produced by A and B.
6. Two very long parallel wires a distance r apart carry identical current I . The distance is now increased to
2r . It is found that the attractive force between them remains the same. What is now the current?
(a)
(b)
(c)
(d)
4.0I
3.2I
2.0I
1.4I
2
7. What is the circulation of the magnetic field
( ò B × d ) on the path indicated in the diagram, which also
shows four infinitely long wires carrying currents of magnitude and directions as indicated?
(a) 2.52 ´10-6 T × m
(b) -2.52 ´10-6 T × m
(c) 1.26 ´10-6 T × m
(d) -1.26 ´10-6 T × m
8. The diagram shows an infinitely long wire carrying current
I directed into the paper, and a straight line segment
carrying the same current running from the left to right. The
total force on the line segment is
(a) 0.15m0 I 2
(b) 0.15m0 I
2
(c) 0.30m0 I 2
(d) 0.30m0 I 2
into the paper
out of the paper
into the paper
out of the paper
9. The diagram shows the cross-section of a cylindrical sample of a diamagnetic
substance placed in a magnetc field directed into the paper. What is the
directions of the induced magnetic field and induced surface current in the
sample?
(a)
(b)
(c)
(d)
Into of the paper and clockwise, respectively
into of the paper and counter clockwise, respectively
out of the paper and clockwise, respectively
out of the paper and counter clockwise, respectively
3
10. A circular wire loop 1.0m in diameter is placed in a region of uniform
magnetic field pointing into the paper as shown. The magnetic field changes
from 5.0T to 2.0T in 30ms . If the electrical resistance of the loop is 50W ,
the induced current in the loop during the 30ms is
(a) 1.57A
(b) 1.57A
(c) 2.83A
(d) 2.83A
clockwise
counter - clockwise
clockwise
counter - clockwise
11. The diagram shows a metal ring moving toward the north end of a
magnet. When viewed at the position shown, the directions of the
induced magnetic field and the induced current are:
(a)
(b)
(c)
(d)
toward the magnet and clockwise, respectively
toward the magnet and counter-clockwise, respectively
away from the magnet and clockwise, respectively
away from the magnet and counter-clockwise, respectively
12. The magnetic flux through a wire loop in the direction pointing into the
paper is given by fm = 5.0cos (3p t ) Wb , where t is in seconds. The
induced emf at t = 0.5s is
(a)
(b)
(c)
(d)
38V
38V
47V
47V
clockwise
counter - clockwise
clockwise
counter - clockwise
4
PART B (52 points)
1. (12 points) Refer to the diagram showing a circular wire loop
of radius 25cm placed on the y-z plane and centered at the
origin. A 4.0Acurrent runs clockwise in the loop. A uniform
magnetic field of 1.6T exists pointing in the y-direction.
(a) (4 points) Find the magnitude and direction of the
magnetic moment vector.
(b) (4 points) Find the magnitude and direction of the torque vector on the loop due to the magnetic
forces, and indicate the direction of motion of the point P on the loop as a result of the torque
(c) (4 points) Find the change of potential energy of the current loop in the magnetic field after the loop
turns through an angle of 90 as a result of the torque.
5
2. (18 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) (4 pts) the magnitude and direction of the magnetic field at
the point P1
(b) (6 pts) the x and y components of the magnetic field at the point P2
(c) (4 pts) the x coordinate (in mm) of a point on the x-axis where the magnetic field is zero.
(d) (4 points) In a separate drawing, indicate with arrows the forces on the wires and find the
magnitudes of these forces if the length of each wire is 60cm .
6
3. (10 pts) Refer to the diagram showing a very long wire with circular
cross-section of radius a carrying a current I pointing out of the
paper uniformly distributed over its cross-section. It is concentrically
surrounded by a very thin cylindrical shell of radius 3a , carrying the
same current I running into the paper.
(a) (6 pts) Find the magnetic field at a distance r from the wire,
separately for the three cases r < a, a < r < 3a, 3a < r .
(b) (4 points) Find the magnetic field at the point r = a 2 and the value of r at another point where the
magnetic field is the same.
7
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 5.0W resistor. The whole assembly is in a uniform
magnetic field B = 2.0T pointing into the paper. At t = 0 , the
rod is given a push so that its initial velocity is 12 m s to the
right.
(a) (6 points) At the time t = 0 , find
(1) the magnitude and direction of the induced current
(2) the power dissipated in the resistor
(3) the magnitude and direction of the force on the rod because of the current
(b) (6 points) Find the time when the velocity is 6.0m / s and the energy dissipated in the resistor up to
this time.
.
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