Magnetic Fields
and Forces -------------------------------------- Joseph F. Alward, PhD Department of Physics University of the Pacific |
Magnetic Fields
One Tesla (T) = 10,000
Gauss ------------------------------------------
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Nicola Tesla (1856-1943) His AC power transmission won over Thomas Edison's DC power. |
Friedrich Gauss (1777-1855) |
Important Equations and People
1. F = ILB sin q 2. F = qvB sin q 3. F = ma 4. a = v2/r 5. B = m0I /2pr ----------------------- Moving charges cause magnetic fields. ----------------------- Magnetic fields exert forces on moving charges. |
Andre Marie Ampere Ampere's Law |
Hans Christian Oersted Discovered magnetic fields. |
Count Ivan Alvardovich (1821-1866) |
Currents Set up Magnetic Fields
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Hans Christian Oersted (1777-1851) |
The Right-Hand Rule for Magnetic
Fields
B-Field of a Current Loop
Another View of the B-Field of a Current Loop
A current loop is the same as a bar magnet; it has north and south faces. B field lines leave north "faces", enter at south "faces". (In this case, the "faces" are left and right side of the circular plane.) |
Rule: If current is counter- clockwise, you're looking at the "north" face of the magnet. |
B-field is strongest at center. From this side of the loop, the inside face of the loop is "north". |
The Electron is a Magnetic Dipole
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The electron spins on its axis,
giving rise to a electron current in the direction of rotation. The electron is like a magnetic dipole, a miniature magnet, with a north end and a south end. |
Magnetic Spin Dipoles in Iron
North and South Cannot Be Isolated
Cutting a magnet in half will not isolate a single north or south. One magnet becomes two, then four, and so on. This process will never |
Magnetic Fields of a Bar Magnet and the Earth
B-field of bar magnet is similar to the Earth's magnetic field. B-field lines leave north face, enter at south face. |
Convection currents inside the earth set up magnetic field. |
Force Between Current Carrying Wires
If currents are in the same direction, wires attract.
If in opposite |
Current Loops Attract and Repel
These current loops are "magnetic dipoles". |
Which sides of loops are north, and which south? |
Bar Magnets
If magnetic dipole loops are oriented the same on neighboring faces, the magnets attract. |
North is attracted to south, and is repelled by north. |
Inducing Magnetism
This is what's happening inside the iron bar to the electron spin magetic dipoles. |
Induced Magnetism
Unaligned dipoles Dipoles aligned Permanent magnet twists iron's magnetic dipoles into alignment with the magnet's B field. |
Magnetic shoes induce magnetism in iron chimney. Both shoes and chimney beneath shoes are now magnets of opposite polarity. |
The Electromagnet and the Doorbell
B-field of current creates strong alignment of magnetic dipoles in iron. |
Paramagnetism
Oxygen is paramagnetic, which means that oxygen molelcules are magnetic dipoles, but at normal temperature, they remain unaligned since their interaction is very weak. Paramagnetism is much weaker than ferromagnetism, which is the magnetism associated with iron, or materials like iron, whose magnetic dipoles interact strongly and align together at room temperature to create a very strong magnetic field. |
Induced Magnetism Recording
Determining Attraction and Repulsion
Magnetic field of current loops twist magnetic dipoles in iron cylinder into alignment, creating an "electromagnet". |
Iron Filings Show Magnetic Field Direction
Magnetic field induces |
Iron filings are tiny bar magnets which line up parallel to B-field lines. |
Compass Needle is a Magnet:
It Aligns with the B-Field
Compass Needle Aligns with Magnetic Field
Magnetic Force on Current-Carrying Wire
F = ILB sin q The direction of the force on the wire may be determined by a second right-hand rule, a right hand rule for magnetic force.
The other right-hand rule |
Using the Second Right-Hand Rule to
Determine Direction of Force
Right-Hand Rule Determines Direction of Force
In which direction, if any, will the metal rod be deflected? |
Torque on a Current Loop in a Magnetic Field
Direct-Current (DC) Motor
CD Motor
Moving Charges in a B-Field
Electric force can be parallel to direction of velocity, but the magnetic force is always perpendicular to the velocity vector. |
Right-Hand Rule for Moving Charges
F = qvB sin q |
Magnetic Force on Moving Charges
F = qvB sin q If the velocity v is parallel to the magnetic field B, the magnetic force is zero because sin q = 0. |
Force on Moving Charges: F = qvB sin q
sin q is positive for any angle between 0 and 180 degrees. |
F = qvB sin q
What is the direction of the force F , if any, in each case? |
Charges Move in Circular Paths
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Circular Paths in Magnetic Fields
Circular Motion in B-Field
Right Hand Rule for Force
Fingers point in direction of Palm shows the direction of |
Mass Spectrometer
F = qvB sin q
(1) q = 90 deg (2) F = qvB (3) F = ma (4) a = v2 /r (5) F = mv2 /r (6) ----------------------- Setting (3) and (6) equal: qvB = mv2 /r (7) m = qBr/v (8) |
Electron Beam in Magnetic Field
Electrons are deflected downward. What is the direction of the magnetic field B? |
Aurora Borealis
Nuclear blasts in the atmosphere will cause auroras (aurorae) at north and south poles. |
Southern Lights: Aurora Australis.
Magnetohydrodynamics
Yamato II |
Ampere's Law
SB|| Dl = m0 I I = net current intersecting the region bounded by the closed path |
Ampere's Law Applied to a Straight Wire
Ampere's Law:
SB|| Dl = m0 I |
B-Field of a Straight Wire
B = m0 I /2pr | m0 = 4p x 10-7 (SI
units) -------------------------------------------- I = 5 A r = 0.02 m |