1. Biot-Savart Law, Ferromagnetism
Physics 122
11/18/2018
Lecture XIV

2. Concepts Superposition Biot-Savart Law – current loop Solenoid
Ferromagnetism
11/18/2018
Lecture XIV

3. Force between two currents
Parallel currents attract
Anti-parallel repel l
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Lecture XIV

4. Superposition d y I x
Two sources of magnetic field – e.g. two currents – add fields as vectors:
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Lecture XIV

5. Biot-Savart Law Infinitesimal length dl carries current I
Magnetic field:
Magnetic field is perpendicular to the plane that contains vectors dl and r.
Use right hand rule B I
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Lecture XIV

6. Current loop
A thin ring of radius R carries current I. Determine the magnetic field on its axis, a distance x from its center. f R f x
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Lecture XIV

7. Current loop=magnetic dipole
For x>>R
The magnetic field goes down as 1/r3 like electric field due to electric dipole
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Lecture XIV

8. Magnetic dipole Current loop = magnetic dipole:
Magnetic dipole is a vector, direction determined by right hand rule:
Fingers along the current
Thumb shows the direction of the magnetic moment
Magnetic field created by magnetic dipole is parallel to the direction of the dipole inside the loop and along the axis(!) m
flow of I
11/18/2018
Lecture XIV

9. Magnetic dipole
When external magnetic field is applied dipoles line up parallel to the field
Minimum of the potential energy at q=0
U=-mBcosq
Magnetic field of the magnetic dipole also is parallel to the external magnetic field,
Thus the total field is increased!
11/18/2018
Lecture XIV

10. Ferromagnetism Electrons inside atoms – little loop currents
When placed inside magnetic field microscopic currents orient to enhance the external field
This effect happens only in some materials – ferromagnetic, e.g. iron.
domains
11/18/2018
Lecture XIV

11. Interactions of Two Current Loops
How will the magnetic dipoles line up?
This effect dominates, because magnetic field is stronger on the axis m m m m ?
Which one is the minimum energy configuration of the top/bottom pairs?
Ask… click to make them fly away.
DEMO: Er-1, coil attracted to bar magnet to show answers… m m m m ?
11/18/2018
Lecture XIV

12. Hysteresis – magnetic memory
After external magnetic field is applied to the ferromagnetic – domains line up and maintain their own magnetic field – natural magnets
Degaus – consecutive application of reversed magnetic field – to “unwind” the domains
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Lecture XIV

13. Magnetic field of a solenoid
Magnetic field inside solenoid can be increased by adding a ferromagnetic core with relative magnetic permeability Km>>1 :
B=Kmm0nI>m0nI
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Lecture XIV

14. Magnetic materials Ferromagnetic Km>>1 (~1000)
Iron, cobalt, nickel, some aloys
residual magnetism can be destroyed (orientation of the domains randomized) by mechanical shock or high T
Paramagnetic Km>1 just a bit (1+10-4,-5)
No domains, but molecules have magnetic moment
Aluminum, magnesium, oxygen, platinum
Diamagnetic Km<1 a really tiny bit (1-10-5,-6)
Molecules do not have a magnetic moment
Copper, diamond, gold, silicon, nitrogen
11/18/2018
Lecture XIV