PHYS 222
Worksheet 20 – Magnetic Materials
Supplemental Instruction
Iowa State University
Leader:
Course:
Instructor:
Date:
Alek Jerauld
PHYS 222
Dr. Paula Herrera-Siklódy
3/6/12
Useful Equations
B  B0  BMagnetization
B  K M B0
BMag  M B0 (M  KM 1)
Net magnetic field inside a material
Magnetic permeability. Permeability: The measure of the
ability of a material to support the formation of a
magnetic field within itself.
Magnetic susceptibility. Susceptibility: The
degree to which a material can be magnetized
in an external magnetic field.
Diamagnetism:
Induced current and magnetic field oppose the applied magnetic field. Very weak: BMag ~ B0 x10-5
Paramagnetism:
Magnetic dipoles tend to line up with the external field. Very weak: B Mag ~ B0 x10-5
Ferromagnetism:
Dipoles prefer to line up with the applied field. There is a collective effect due to domain
dipoles. Very strong: BMag ~ B0 x105
Related Problems
1) Label the following materials as Paramagnetic, Ferromagnetic, or Diamagnetic based on
their magnetic susceptibilities:
Bismuth (-16.6 x 10-5)
Diamagnetic (small, negative susceptibility)
Aluminum (2.2 x 10-5)
Paramagnetic (small, positive susceptibility)
Oxygen Gas (0.19 x 10-5)
Paramagnetic (small, positive susceptibility)
Iron (3000)
Ferromagnetic (Large, Positive susceptibility)
Lead (-1.8 x 10-5)
Diamagnetic (small, negative susceptibility)
2) A long solenoid with 61 turns of wire per centimeter carries a current of 0.16 A. The wire
that makes up the solenoid is wrapped around a solid core of silicon steel (KM = 5200). (The
wire of the solenoid is jacketed with an insulator so that none of the current flows into the
core.) (Book 28.49)
(a) For a point inside the core, find the magnitude of the magnetic field B0 due to the
solenoid current.
B  0 nI  0.0012 T
(b) For a point inside the core, find the magnitude of the magnetization, M
You do not need to know Magnetization, M. (Ignore this question)
(c) For a point inside the core, find the magnitude of the total magnetic field B.
B  K M B0  5200(0.0012)  6.4 T
3) A magnetic field Bo is applied to a paramagnetic substance. In the interior of the
substance the portion of the magnetic field produced by the magnetic dipoles of the
substance is: (S11 Exam 2)
(a) greater than Bo and in the same direction
(b) less than Bo and in the same direction
(c) less than Bo and in the opposite direction
(d) greater than Bo and in the opposite direction
(e) the same as Bo
For a paramagnet, the total field inside is greater than the applied field and points in
the same direction—however, the portion produced by the dipoles is small compared
to the applied field. Therefore, it is less than Bo and in the same direction.
Additional Problems using Faraday’s Law and Lenz’s Law:
4) A 6.0-cm-long flashlight battery has an emf of 1.5 V. A 6.0-cm-long wire moves through
a 0.10 T magnetic field and creates a motional emf of 1.5V. What speed must this wire
have? (S11 Exam 2)
(a) 250m/s
(b) 2.5m/s
(c) 0.25m/s
(d) 25m/s
d


 BdA  Blv  v 
 250 m / s
dt
Bl
5) A flat, square loop (0.1 m on a side) is in a region of space that has a magnetic field that
points into the page. Between t = 0 s and t = 5 s the magnetic field is decreasing, at a
constant rate, from 10 T to 0 T. The loop has a resistance of 4 Ω. At t = 3 s, what is the size
and direction of the current flowing in the loop? (F09 Exam 2)
(a) 5 × 10-2 A, clockwise
(b) 5 × 10-2 A, counterclockwise
(c) 5 × 10-1 A, clockwise
(d) 5 × 10-1 A, counterclockwise
(e) none of the above
dB 0  10

 2 T / s
dt
5
d  dB


A  2(0.1) 2  0.02 V
dt
dt
I

 5 mA
R
B-field is decreasing going into page, so B-induced should point into the page, thus Iinduced should be Clockwise.
6) A bar magnet is dropped through a wire loop as shown below. At the moment shown
when the magnet is still above the loop, will there be any
current in the wire loop and if so, which direction will the
current be? (S09 Exam 2)
(a) no current in loop
(b) current is clockwise (when viewed from above)
(c) current is counter-clockwise (when viewed from above)
The B-field from the bar-magnet leaves the north-pole of
the magnet. When viewed from above, the B-field is into the
page and increasing in strength. Hence the flux is increasing
=> induced current will try to oppose the change by creating a
B-field within the loop that is out of the page.
7) A U-shaped wire, see below, has a movable wire AB connected to it. This
arrangement is in a uniform field perpendicular to, and into, the page. If the magnetic
field strength is 40T, what is the magnitude of the induced EMF (in volts) and the
direction of the induced current when AB is moving to the right at 20 cm/sec? (S09 Exam 2)
(a) 0.16 V, counter-clockwise when viewed from above
(b) 0.16 V, clockwise when viewed from above
(c) 1600 V, counter-clockwise when viewed from above
(d) 1600 V clockwise when viewed from above
(e) 0 V, no induced current
d
dA
B
 BvL  0.16 V
dt
dt
Induced current opposes change, so it creates a B-filed that is out of the page within the
loop => counterclockwise current.
