<< Chapter < Page Chapter >> Page >

Check Your Understanding Repeat the calculations from the previous example for I 0 = 0.040 A .

a. 1.0 × 10 −4 T ; b. 0.60 T; c. 6.0 × 10 3

Got questions? Get instant answers now!


  • Materials are classified as paramagnetic, diamagnetic, or ferromagnetic, depending on how they behave in an applied magnetic field.
  • Paramagnetic materials have partial alignment of their magnetic dipoles with an applied magnetic field. This is a positive magnetic susceptibility. Only a surface current remains, creating a solenoid-like magnetic field.
  • Diamagnetic materials exhibit induced dipoles opposite to an applied magnetic field. This is a negative magnetic susceptibility.
  • Ferromagnetic materials have groups of dipoles, called domains, which align with the applied magnetic field. However, when the field is removed, the ferromagnetic material remains magnetized, unlike paramagnetic materials. This magnetization of the material versus the applied field effect is called hysteresis.

Key equations

Permeability of free space μ 0 = 4 π × 10 −7 T m/A
Contribution to magnetic field
from a current element
d B = μ 0 4 π I d l sin θ r 2
Biot–Savart law B = μ 0 4 π wire I d l × r ^ r 2
Magnetic field due to a
long straight wire
B = μ 0 I 2 π R
Force between two parallel currents F l = μ 0 I 1 I 2 2 π r
Magnetic field of a current loop B = μ 0 I 2 R (at center of loop)
Ampère’s law B · d l = μ 0 I
Magnetic field strength
inside a solenoid
B = μ 0 n I
Magnetic field strength inside a toroid B = μ o N I 2 π r
Magnetic permeability μ = ( 1 + χ ) μ 0
Magnetic field of a solenoid
filled with paramagnetic material
B = μ n I

Conceptual questions

A diamagnetic material is brought close to a permanent magnet. What happens to the material?

Got questions? Get instant answers now!

If you cut a bar magnet into two pieces, will you end up with one magnet with an isolated north pole and another magnet with an isolated south pole? Explain your answer.

The bar magnet will then become two magnets, each with their own north and south poles. There are no magnetic monopoles or single pole magnets.

Got questions? Get instant answers now!


The magnetic field in the core of an air-filled solenoid is 1.50 T. By how much will this magnetic field decrease if the air is pumped out of the core while the current is held constant?

Got questions? Get instant answers now!

A solenoid has a ferromagnetic core, n = 1000 turns per meter, and I = 5.0 A. If B inside the solenoid is 2.0 T, what is χ for the core material?


Got questions? Get instant answers now!

A 20-A current flows through a solenoid with 2000 turns per meter. What is the magnetic field inside the solenoid if its core is (a) a vacuum and (b) filled with liquid oxygen at 90 K?

Got questions? Get instant answers now!

The magnetic dipole moment of the iron atom is about 2.1 × 10 −23 A · m 2 . (a) Calculate the maximum magnetic dipole moment of a domain consisting of 10 19 iron atoms. (b) What current would have to flow through a single circular loop of wire of diameter 1.0 cm to produce this magnetic dipole moment?

2.1 × 10 −4 A · m 2
2.7 A

Got questions? Get instant answers now!

Suppose you wish to produce a 1.2-T magnetic field in a toroid with an iron core for which χ = 4.0 × 10 3 . The toroid has a mean radius of 15 cm and is wound with 500 turns. What current is required?

Got questions? Get instant answers now!

A current of 1.5 A flows through the windings of a large, thin toroid with 200 turns per meter. If the toroid is filled with iron for which χ = 3.0 × 10 3 , what is the magnetic field within it?

0.18 T

Got questions? Get instant answers now!

Questions & Answers

A closely wound search coil has an area of 4cm^2,1000 turns and a resistance of 40ohm. It is connected to a ballistic galvanometer whose resistance is 24 ohm. When coil is rotated from a position parallel to uniform magnetic field to one perpendicular to field,the galvanometer indicates a charge
Palak Reply
Using Kirchhoff's rules, when choosing your loops, can you choose a loop that doesn't have a voltage?
Michael Reply
how was the check your understand 12.7 solved?
Bysteria Reply
LOAK Reply
he's the father of 3 newton law
he is Chris Issaac's father :)
how to name covalent bond
Bryan Reply
what do you understand by the drift voltage
Brunelle Reply
what do you understand by drift velocity
well when you apply a small electric field to a conductor that causes to add a little velocity to charged particle than usual, which become their average speed, that is what we call a drift.
drift velocity
what is an electromotive force?
Danilo Reply
It is the amount of other forms of energy converted into electrical energy per unit charge that flow through it.
How electromotive force is differentiated from the terminal voltage?
in the emf power is generated while in the terminal pd power is lost.
what is then chemical name of NaCl
Sagar Reply
sodium chloride
sodium chloride
Sodium Chloride.
How can we differentiate between static point and test charge?
Comfort Reply
Wat is coplanar in physics
Humble Reply
two point charges +30c and +10c are separated by a distance of 80cm,compute the electric intensity and force on a +5×10^-6c charge place midway between the charges
Tijani Reply
what is the difference between temperature and heat
Ishom Reply
Heat is the condition or quality of being hot While Temperature is ameasure of cold or heat, often measurable with a thermometer
Temperature is the one of heat indicators of materials that can be measured with thermometers, and Heat is the quantity of calor content in material that can be measured with calorimetry.
the average kinetic energy of molecules is called temperature. heat is the method or mode to transfer energy to molecules of an object but randomly, while work is the method to transfer energy to molecules in such manner that every molecules get moved in one direction.
2. A brass rod of length 50cm and diameter 3mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250°c( degree Celsius) if the original length are 40°c(degree Celsius) is there at thermal stress developed at the junction? The end of the rod are free to expand (coefficient of linear expansion of brass = 2.0×10^-5, steel=1.2×10^-5k^1)
A charge insulator can be discharged by passing it just above a flame. Explain.
Mudassar Reply
of the three vectors in the equation F=qv×b which pairs are always at right angles?
Practice Key Terms 6

Get the best University physics vol... course in your pocket!

Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 2' conversation and receive update notifications?