Unit 7: Sources of magnetic field Oersteds experiment. Biot and - - PowerPoint PPT Presentation

Unit 7: Sources of magnetic field

• Oersted’s experiment.
• Biot and Savart’s law.
• Magnetic field lined
• Magnetic field created by a circular loop
• Ampère’s law (A.L.). Applications
• Straight current-carrying wire
• Coil

Jean-Baptiste Biot Félix Savart André Marie Ampère

Oersted’s experiment. 1820

Tipler, chapter 27,2

• 1. If switch is off, there isn’t

current and compass needle is aligned along north-south axis

• 2. If switch is on, current

aligns compass needle perpendicular to current.

• 3. If current flows in opposite

direction, compass needle is aligned in opposite direction.

An electric current creates a magnetic field

F F

Biot and Savart’s law

• Magnetic field created by a

current is perpendicular to current, and depends on the intensity of current and distance from current.

Tipler, chapter 27-2

• Magnetic field created by a

current element (Idl ) at a point P is:

B  d

i

P

2 r 3

r d i 4 r d i 4 d u l r l B             

dl direction is the same as i 0 (vacuum magnetic permittivity)=410-7 Tm/A

r

r

r u   

r 

l  d



 

B A 3

r d 4 i r l B     

• Magnetic field created by a finite piece of wire is the

sum (integral) of each current element at P:

l  d

B 

i

A B

Biot and Savart’s law

P

This equation can be applied to different conductor shapes, straight conductors, circular conductors,…….

r 

i

Tipler, chapter 27.2

• Magnetic field lines created by a straight current-

carrying wire are circular in shape around conductor:

Magnetic field lines

Direction of magnetic field comes from right-hand or screw rule

B 

B  B 

• Magnetic field lines created

by a circular loop:

i

Magnetic field lines

https://www.youtube.com/watch?v=V-M07N4a6-Y

B  B  B 

• As magnetic poles cannot exist isolated (north pole or

south pole), any field line exiting from a north pole must go to a south pole, and all magnetic field lines are closed lines.

Magnetic field lines

• Ampère’s law relates the integral of magnetic field

along a closed line and the intensity passing through a surface enclosed by this line. Closed line C must be chosen by us (if possible, should be a magnetic field line):

 

 

c i i

I d  l B  

I1 I2 Ii ... c

Tipler, chapter 27.4

Ampère’s law.

Ampère’s law

• Each intensity has it own sign, according to the

r¡ght-hand or screw rule.

• Ampère’s law is equivalent (in Electromagnetism), to Gauss’s

law in Electrostatics.

I1>0 I2>0 Ii<0 c I>0 ...

Ampère’s law.

• It’s used to compute magnetic fields where symmetry

exists.

• In order to easily compute the integral of line, the

chosen closed line C should have two features:

• a) Modulus of magnetic field should be equal at every

points on closed line C.

• b) Magnetic field vector (B) should be parallel to closed

line C at every points along C.

• In this way: 

 

   

c c c

BL dl B Bdl dl B  

Ampère’s law.

i

• Let’s take a straight current-carrying wire. Field

lines

• f

this conductor are circumferences. Choosing one of such lines of radius R, surface enclosed by such line and applying A.L:

R

B B B B L

I R 2 B dl B d

L L

      

 

l B  

R 2 I B   

Tipler, chapter 27.4

Application of A.L: straight current-carrying wire.

• A conductor creates a magnetic field on second conductor

and a force appears on this conductor. The same happens

• n first conductor.

Tipler, chapter 27.4

Force between two straight current-carrying wires

d I2 I1  B2  B1  F21  F12  

http://www.youtube.com/watch?v=43AeuDvWc0k

R 2 Ni B   

• Applying A.L. to middle line of toroid and to circle

enclosed by this line:

Tipler, chapter 27.4

i i

R

N turns

B

NI R 2 B dl B d

L L

      

 

l B  

Application of A.L: toroid (circular solenoid).

By applying A.L. at points outside

• f toroid, result is that magnetic

field is zero at any point outside toroid.  B=0  B=0

B B B

ni L Ni B    

• If L>>>r, the magnetic field inside a solenoid can be taken as

uniform, and null outside the solenoid. From toroid (L=2R):

Application of A.L: solenoid.

L N n 

Number of turns by unit of lenght

S Ni    

Magnetic moment of a solenoid: Magnetic moment by unit of volume inside a solenoid is called magnetization:

B SL S Ni V M         

B r

B B

L

N turns