<< 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!

Summary

  • 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!

Problems

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?

317.31

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

what are waves
KENNETH Reply
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities
Abdikadir
Discuss how would orient a planar surface of area A in a uniform electric field of magnitude E0 to obtain (a) the maximum flux and (b) the minimum flux through the area.
KARAN Reply
I'm just doing the first 3 with this message. but thankyou for the time your obviously intending to support us with. viva la accumulation
Marcel
Find the net capacitance of the combination of series and parallel capacitors shown belo
jean Reply
what is ohm?
Sharafat Reply
calculate ideal gas pressure of 0.300mol,v=2L T=40°c
Viola Reply
what is principle of superposition
Jyoti Reply
what are questions that are likely to come out during exam
King Reply
what is electricity
Jyoti Reply
watt is electricity.
Adam
electricity ka full definition with formula
Jyoti
If a point charge is released from rest in a uniform electric field will it follow a field line? Will it do so if the electric field is not uniform?
Sadaqat Reply
Maxwell's stress tensor is
Ami Reply
Yes
doris
neither vector nor scalar
Anil
if 6.0×10^13 electrons are placed on a metal sphere of charge 9.0micro Coulombs, what is the net charge on the sphere
Rita Reply
18.51micro Coulombs
ASHOK
Is it possible to find the magnetic field of a circular loop at the centre by using ampere's law?
Rb Reply
Is it possible to find the magnetic field of a circular loop at it's centre?
Rb Reply
yes
Brother
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
Gifty Reply
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
Gifty
Under which topic
doris
what is electrostatics
Yakub Reply
Study of charges which are at rest
himanshu
Practice Key Terms 6

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play




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?

Ask