lf magnetic field

PHYSICS 271Magnetic Field

New Era University – Virtual Learning EnvironmentCollege of Engineering & Technology

IntroductionIn previous module, we discussed the sources of magnetic force. To complete the description of the magnetic interaction, this module explores the sources of magnetic fields. The law of Biot and Savart will be discussed and used to calculate the magnetic field produced at some point in space by a small current element. Using the principle of superposition, the total magnetic field due to various current distributions will be obtained. Also, the force between two current carrying wires will be discussed including the magnetic fields each wire produced. Ampere’s Law will also be discussed which is useful in calculating the magnetic field of a highly symmetric configuration carrying a steady current. Moreover, this module is concerned with the magnetic properties of each magnetic materials.

This file is for exclusive use in Physics271-NEU by LDH

04/18/2023This file is for exclusive use in Physics271-NEU by LDH

SUB-TOPICS

• Magnetic Field Concepts

• Sources of Magnetic Field

• Magnetic Field of the Earth

• Magnetic Materials

• Ferromagnetism

• Sample Problems

• Assessment

Magnetic Fields

Course Objectives:At the end of the week, the student should be able to 1. Classify substances in relation to its magnetic properties.2. Identify the various sources of magnetic fields3. Apply Ampere’s law and Biot-Savart Law in magnetism4. Calculate the magnitude of a magnetic field from different sources

04/18/2023 This file is for exclusive use in Physics271-NEU by LDH

Magnetic Fields

Magnetic Field Concepts


The magnetic field caused by a short segment dl of a current carrying conductor can be obtained using the principle of superposition of magnetic fields . This is where Biot and Savart law was derived. The total magnetic field B is B = ∫dB = ∫μo I dl x ȓ

4π r2

where dl is a vector of length dl in the same direction as the current.

1.Magnetic Field due to current element in a conductor

dl


http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/magfie.html

http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/amplaw.html

From the equation

B =

B = (I dl sin ϴ ) r2

where ϴ = angle between the vector dl in the direction of the current

and unit vector ȓ r = distance from the small segment dl to the field point P

….Magnetic Field due to current element in a conductor

dl

∫ȓϴ


The magnetic field of an infinitely long straight wire can be obtained by applying Ampere's law. Ampere's law takes the form and for a circular path entered on the wire, the magnetic field is everywhere parallel to the path. The summation then becomes

2.Magnetic Field due to current carrying conductor



http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/magcur.html


…Magnetic Field due to current carrying conductor

B=μI/2πr

Where: B=Magnetic Field μo = permeability in free space

I = Current in the wire r = radial distance


Solution:This is an application of finding the magnetic field produced by a current carrying conductor that exerted a magnetic force on a moving charge. This force given by F = qvB sin θ where θ is the angle between the velocity of the moving charge and the magnetic field. This angle θ is 90º. First we obtain the magnitude of the magnetic field,

B = μI/2πR = (4π x 10-7 Tm/A)(3.0A) / 2π(0.050 m) = 1.2 x 10-5 TThen,

F = (6.5 x 10-6 C)(280 m/s)(1.2 x 10-5 T) sin 90º = 2.18 x 10-8 N Assuming the current in the wire is moving up then the magnetic field is directed into the page thus magnetic force exerted on the charge particle by the current on the wire is directed towards the wire, hence, the charge particle is drawn towards the wire.


A long, straight wire is carrying a current of 3.0 A. A particle has a charge of +6.5 x 10-6 C and is moving parallel to the wire at a distance of 0.050 m. The speed of the particle is 280 m/s. Determine the magnitude and direction of the magnetic force exerted on the charged particle by the current in the wire.

Sample Problem 1

3. Magnetic Field due to current carrying loop

B=μI/2R

The form of the magnetic field from a current element in the Biot-Savart law becomes



http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/biosav.html

…. Magnetic Field due to current carrying loop

B=μI/2R

Where: B=Magnetic Field μo = permeability in free space

I = Current in the wire R = Radius of the loop


Solution:This is magnetic field due to current carrying loop, hence, we use

B = μI/2R where μ = 4π x 10-7 Tm/A and l = 0.400 m = 2πR, hence, R=0.400/2π=0.064 m

= (4π x 10-7 Tm/A)(10.0A) / [2(0.064 m)]B = 9.8 x 10-5 T

Note: Referring to Problem #5 of Chapter 30 pp 957 (by Jewett & Serway). This problem is an extension of a square loop conductor having length l = 0.400 m which gives a perimeter of the square loop equal to 1.6 m. Using this value of perimeter in a circular turn, R = 1.6 / 2 π= 0.255 m. This gives us B=24.7 x 10-6 T. This note is to distinguish the difference between what was written in the outline as a problem and what was written in the book.


Sample Problem 1A conductor in the shape of a single circular turn of length l = 0.400 m carries a current I =10.0 A (in clockwise direction). Calculate the magnitude and direction of the magnetic field at the center of the circle.

4. Magnetic Field from “SOLENOID”

A long straight coil of wire can be used to generate a nearly uniform magnetic field similar to that of a bar magnet.

n is the number of turns per unit length, sometimes called the "turns density".



http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/elemag.html

…. Magnetic Field from “SOLENOID”Taking a rectangular path about which to evaluate Ampere's Law such that the length of the side parallel to the solenoid field is L gives a contribution BL inside the coil. This admittedly idealized case for Ampere's Law gives



The field can be greatly strengthened by the addition of an iron core. Such cores are typical in electromagnets.

5. Magnetic Field from “IRON-CORE SOLENOID”

μ = μR μo where : μo= 4π x 10-7 T ∙m/AμR =relative permeability of

the core n = turns density = N/L

B= μnI =μR μonI




B= μRμonI

... Magnetic Field from “IRON-CORE SOLENOID”


ElectromagnetElectromagnets are usually in the form of iron core solenoids. The ferromagnetic property of the iron core causes the internal magnetic domains of the iron to line up with the smaller driving magnetic field produced by the current in the solenoid. The effect is the multiplication of the magnetic field by factors of tens to even thousands.



http://hyperphysics.phy-astr.gsu.edu/HBASE/solids/ferro.html



http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/solenoid.html

5. Magnetic Field of the Earth

The Earth's magnetic field is similar to that of a bar magnet tilted 11 degrees from the spin axis of the Earth.




So how did the Earth get its magnetic field?

Magnetic fields surround electric current, so probably, the circulating electric currents in the Earth's molten metalic core are the origin of the magnetic field. A current loop gives a field similar to that of the earth. The rotation of the Earth plays a part in generating the currents which are presumed to be the source of the magnetic field. The magnetic field magnitude measured at the surface of the Earth is about half a Gauss. The Earth's magnetic field is attributed to a dynamo effect of circulating electric current, but it is not constant in direction. Rock specimens of different age in similar locations have different directions of permanent magnetization. Evidence for 171 magnetic field reversals during the past 71 million years has been reported.


Magnetic Materials1. Diamagnetic – substance which decreases the

magnetic field of a current. The atoms do not possess a μ. They are repelled by magnets. Example: copper & silver

2. Paramagnetic - substance which increases the magnetic field of a current. The atomsdo possess μ. Attracted by magnets. Example: Aluminum & Platinum

3. Ferromagnetic - substance with greater μ that is hundreds or even thousand times. Exhibits a high degree of magnetizing ability. Attracted by magnets. Example:Nickel, Cobalt and many

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FerromagnetismIron, nickel, cobalt and some of the rare earths (gadolinium, dysprosium) exhibit a unique magnetic behavior which is called ferromagnetism because iron (ferrum in Latin) is the most common and most dramatic example. Samarium and neodymium in alloys with cobalt have been used to fabricate very strong rare-earth magnets.


http://hyperphysics.phy-astr.gsu.edu/HBASE/solids/magperm.html

FerromagnetismFerromagnetic materials exhibit a long-range ordering phenomenon at the atomic level which causes the unpaired electron spins to line up parallel with each other in a region called a domain.




FerromagnetismWithin the domain, the magnetic field is intense, but in a bulk sample the material will usually be unmagnetized because the many domains will themselves be randomly oriented with respect to one another. Ferromagnetism manifests itself in the fact that a small externally imposed magnetic field, say from a solenoid, can cause the magnetic domains to line up with each other and the material is said to be magnetized. The driving magnetic field will then be increased by a large factor which is usually expressed as a relative permeability for the material. A magnetic field of about 1 T can be produced in annealed iron with an external field of about 0.0002 T, a multiplication of the external field by a factor of 5000!





Ferromagnetism

Ferromagnets will tend to stay magnetized to some extent after being subjected to an external magnetic field. This tendency to "remember their magnetic history" is called hysteresis. The fraction of the saturation magnetization which is retained when the driving field is removed is called the remanence of the material, and is an important factor in permanent magnets.All ferromagnets have a maximum temperature where the ferromagnetic property disappears as a result of thermal agitation. This temperature is called the Curie temperature.


http://hyperphysics.phy-astr.gsu.edu/HBASE/solids/hyst.html

http://hyperphysics.phy-astr.gsu.edu/HBASE/solids/magperm.html


Magnetic Forces Between Wires

Note that two wires carrying current in the same direction attract each other, and they repel if the currents are opposite in direction. Once you have calculated the force on wire 2, of course the force on wire 1 must be exactly the same magnitude and in the opposite direction according to Newton's third law.


http://hyperphysics.phy-astr.gsu.edu/HBASE/newt.html

Assessment:

2. Assuming the current in a certain wire is moving down then a charged particle to the left of the wire will experience a magnetic field is directed

a. into the page b. out of the page c. towards the wire d. away from the wire

1. For a current carrying wire, the greater the distance from which you are to measure the magnetic field created by the wire directed in concentric circles around it, the

a. stronger is the field b. weaker is the field c. stronger is the current d. weaker is the current

3. Thus magnetic force exerted on the charge particle mentioned in item #2 is directed a. into the page b. out of the page c. towards the wire d. away from the wire

4. For a current carrying loop, the greater the radius of the loop, the a. stronger is the field b. weaker is the field c. stronger is the current d. weaker is the current

5. The magnetic field from a solenoid is similar to that of a bar magnet. The field is a. weaker inside the solenoid b. concentrated inside the solenoid c. divergent inside the solenoid d. stronger outside the solenoid


Assessment:6. For an iron-core solenoid, the magnetic field is given by B= μR μo nI, where μo is called permeability in free space. This is equal to a. 4π x 10-7 T m/A∙ b. 4 x 10-7 T m/A∙ c. 4π x 107 T m/A∙ d. π x 107 T m/A∙

7. Scientist speculated that the Earth's magnetic field is attributed to a dynamo effect of circulating electric current in the Earth's molten metallic core. This is effect is similar to a. moving charges b. current carrying loop c. long straight current carrying wires c. moving conductors

8. Aluminum and platinum are examples of a. diamagnetic materials b. paramagnetic materials c. ferromagnetic materials d. All of these

9. It is a property of ferromagnetic materials to stay magnetized to some extent after being subjected to an external magnetic field. This tendency to "remember their magnetic history is called a. relative permeability b. hysteresis c. remanence d. magnetic domain


Assessment:

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10. It refers to a loop of wire wrapped around a metallic core, which produces a magnetic field when an electric current is passed through it.

a. Coil b. corec. Solenoid d. iron-core solenoid

11. The following materials are diamagnetic EXCEPTa. Mercury b. Copperc. Silver d. Uranium

12. Ferromagnetic materials are widely used ina. electromagnets b. motors and generatorsc. Transformers cores d. all of these

13. Two straight long vertical wires W1 and W2 carry steady currents I and 3I, respectively, as shown. P is the point midway between the wires. The resultant magnetic field at P due to the currents in the wires is B. The direction of B at point P is W1 W2

a.Vertically upb. horizontal and directed towards wire 2 ∙ Pc. Horizontal and directed normally into the plane of the paper (away from you) I 3Id. Horizontal and directed normal to the plane of the paper (towards you)

Assessment:14. Four solinoids have the same number of loops. Which solenoid would produce the strongest magnetic field? a. the solenoid with 1 A of current b. the solenoid with 100 A of current

c. the solenoid with 10 A of current d. the solenoid with 0.10 A of current 15. Electric motor work by placing a(n) _____ between the poles of a permanent magnet. a. armature b. electromagnet c. galvanometer d. long wire

16. What would induce a greater electric current in the wire? a. adding more loops of wire b. removing loops of wire

c. Pulling the magnet out of the loop rather than pushing it ind. Pushing the magnet into the loop rather than pulling it out


These questions are of low and medium level of cognitive complexity to measure the learning of the students after the discussion. When you score below 12 points, you should review this topic and understand the concept of magnetic fields and its sources before proceeding to solve questions/exercises of higher level of cognitive complexity.


References:1.Cutnell & Johnson, Physics, 2007 pp.662-6762.Serway & Jewett, Physics for Scientist and Engrs., 2008 pp. 927-9553. Tipler, Physics for Scientist& Engrs., 2004 pp. 883-901,908- 916

lf magnetic field

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