Download Exam 4

Physics 196 Fall 2011
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 4.0mm short wire at the origin of a right hand rectangular coordinate system carries
a current of 8.0A in the direction shown. Find the magnetic field it creates at the point
P on the x-y plane as indicated.
(a) 1.3´10-10 k̂ (T )
(b) -1.3´10-10 k̂ (T )
(c) 9.1´10-11 k̂ (T )
(d) -9.1´10-11 k̂ (T )
2. A circular loop carrying 5.0A current creates a magnetic field of 2.0T at the center. What is the radius of
the loop?
(a) 0.50m
(b) 0.79m
(c) 1.57m
(d) 1.96m
3. A long thin solenoid is formed by tightly winding copper wire of diameter 2.5mm onto a hollow cylindrical
surface of radius 1.5cm. When a 7.0A current runs in the wire, what is the magnetic field inside the
solenoid?
(a) 3.52mT
(b) 2.70mT
(c) 1.39mT
(d) 0.88mT
1
4. A 20.0A current runs to the right in a very long wire. What is the
magnetic field at the point indicated?
(a)
(b)
(c)
(d)
40T
40T
80T
80 T
int o paper
out of paper
i nt o paper
out of paper
5. A tiny loop of area 3.0 ´10-6 m2 carrying 2.0A current is placed 1.0m from
an infinitely long wire carrying current of 100A as shown. The loop and
the wire lie on the same plane. The torque on the loop is
(a)
(b)
(c)
(d)
0J
1.6 ´1010 J
2.5´1010 J
3.8´1010 J
6. The force of attraction between two very long parallel wires a distance r apart with identical current I is
F . What is the force of attraction if the currents are increased to 2I and the distance is reduced to r 2 ?
(a)
(b)
(c)
(d)
F /8
F/4
4F
8F
2
7. A very long solenoid carries a 5.0A current in its wire in
the direction as shown. What is the circulation of its
 
magnetic field  B  d  on the path indicated?
(a)
(b)
(c)
(d)
-1.9 ´10-5 T × m
+1.9 ´10-5 T × m
-3.8´10-5 T × m
+3.8´10-5 T × m
8. The density of a certain metal is 2.5g / cc . Its atom has mass number 23 and magnetic moment 0.4 Bohr
magneton. What is its saturation magnetic field?
(a)
(b)
(c)
(d)
0.4 T
0.3 T
0.2 T
0.1T
9. A wire is wound on a copper cylinder, and carries current in the direction
shown. Given that copper is diamagnetic, how does the direction of
magnetization appear when viewed in the position indicated?
3
10. A circular wire loop of radius 30.0cm is placed in a region of uniform
magnetic field of 2.0T perpendicular to it. The loop is turned through
180 in the direction shown in a time of 5.0s. The average induced emf
during this time interval is
(a)
(b)
(c)
(d)
0.15 V
0.23 V
0.37 V
0.44 V
11. A triangular wire frame as shown enters a half space where there is a uniform
magnetic field B into the paper. The frame travels with constant velocity u to
the right. What is the induced emf in the frame when its leading vertex has
penetrated a distance x into the magnetic field region? (Hint: start with the
relation between x and t , where t is the time since the vertex enters the region.)
(a)
(b)
(c)
(d)
Bx 2u
2Bx 2u
Bxu
2Bxu
12. A permanent magnetic moves away from an observer as
shown. The direction as seen by the observer of the induced
current on a ring between the magnet and the observer is
(a) clockwise
(b) counter-clockwise
13. In a typical MRI machine, the magnetic field is
and the frequency of the radio wave is
I found this from the website(other than Wikipedia): http://
4
PART B (48 points)
1. (14 pts) Refer to the diagram showing two infinitely long currentcarrying wires parallel to the z-axis. The positions and directions of
the currents are indicated. Find
(a) (4 pts) the magnitude and direction of the magnetic field at the
origin
(b) (6 pts) the x and y components of the magnetic field at the point P
(c) (4 pts) the y coordinate of a point on the y-axis where the magnetic field is zero.
5
2. (8 pts) A long coaxial cable consists of a wire of radius a surrounded by a
cylindrical shell of inner radius b and outer radius c . The wire carries
current I out of the paper while the shell carries the same current in the
opposite direction. Both currents are uniformly distributed.
(a) (3 pts) Find the current densities in the wire and in the shell.
(b) (5 pts) Find the magnetic field at a distance r from the axis, separately for the four cases
r < a, a < r < b, b < r < c, c < r . Express your answers in terms of I .
6
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. As shown, the magnetic field is pointing into the paper
and varies with time according to the equation B = 2.0sin ( 4p t ) where B is
in Tesla and t is in seconds.
(a) (4 points) With the normal for the loop chosen to point out of the
paper, write expressions for (1) the magnetic flux through the loop, (2)
the induced emf, and (3) the induced current at the time t
(b) (2 points) Find the induced current at t  1/ 4s . Indicate its direction as clockwise or counterclockwise
(c)( 3 points) Sketch the magnetic flux and the current as functions of time between t  0 and t  1/ 4s
(d) (3 points) Find the total charge that has gone through any point on the loop from the time t = 0 and
t  1 / 8s
7
4. (14 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 out
of the paper. Starting at t = 0 , when the rod is at rest, a constant force
F  0.05 N is applied to the rod in the direction shown.
(a) (8 pts) At the time when the velocity of the rod reaches 6.0m / s ,
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
(4) the power delivered by the force F
(b) (4 points) Show that the velocity of the rod obeys a differential equation in terms of m , L , R , B
and F that is similar to that of the charging of a capacitor.
.
(c) (2 points) Why are the answers in (a)(2) and (a)(4) different?
8