Magnetic Fields  and Forces -------------------------------------- Joseph F. Alward, PhD     Department of  Physics   University of the Pacific

 Magnetic Fields                                                                 

One Tesla (T) = 10,000 Gauss ------------------------------------------ Source Magnetic Field         (Gauss) Earth          0.5 Appliance          10 Bar magnet         100 Human limit       2000 Large electro- magnet     50,000

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   

This is the first of two right-hand rules dealing with magnetism and magnetic forces.

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              

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 end; even when the last electron spin dipole is reached, it cannot be cut to reveal a single north or single south pole.

 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 direction, wires repel.  This is the opposite of the rule for charges: like charges repel, opposite charges attract.  Using the two right hand rules, one for finding thedirection of the B-field of a wire, and the other for the direction of force on a wire, one can predict the results above.

 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  magnetism in iron filings.

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 gave the direction of the magnetic field B.

    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                                 

   Circular Paths in Magnetic Fields                                 

   Circular Motion in B-Field           

Right Hand Rule for Force Fingers point in direction of magnetic field B. Thumb points in direction of the velocity vector v. Palm shows the direction of the force F.

  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 I = net current intersecting      the region bounded by      the closed path -------------------------- B|| = constant = B SB|| Dl = B SDl              = B (2pr) B (2pr) = m0 I B = m0 I /2pr

  B-Field of a Straight Wire 

B = m0 I /2pr

m0 = 4p x 10-7 (SI units) -------------------------------------------- I = 5 A r = 0.02 m B = (4p x 10-7) (5)/[(2p)(0.02)]    = 50 x 10-6 T    = 0.50 x 10-4    = 0.50 gauss (about the same as Earth's field) --------------------------------------------- What is the B field at 0.04 m?