"It is a good morning exercise for a research scientist to discard a pet hypothesis every day before breakfast"
Konrad Lorenz

• Magnetic Poles.
  
  
  • Somewhat analagous to positive and negative electric charges a magnet is said to have a North(N) and a South(S) pole.  A magnetic field may be represented by "magnetic field lines" which begin at a North pole and end on a South pole, in exactly the same way as electric field lines begin and end on positive and negative charges.
    
    
  • Unlike positive and negative electric charges, magnetic North and South poles cannot be isolated.  Breaking a magnet into two creates two magnets, each with a North and South pole.  This is true even down to the atomic level.  Technically we state "there are no magnetic monopoles"

• As we have seen a magnetic field can most easily be created by the moving charges that constitute an electric current.  The form of the magnetic field produced in this way is given by Ampere's Law, which can be considered the magnetic equivalent of Coulomb's Law.  The general mathematical form of Ampere's Law is beyond the scope of this course, however, there are several special cases of currents creating magnetic fields we will consider;

• Magnetic field due to a long straight wire carrying current .

The magnitude of the magnetic field (in a vacuum) B, at a distance r from the wire carrying current, I, is given by



where, µ_o is a constant known as the permeability of the vacuum, having the value 4 π x 10^-7 Tesla.m/A. [The Tesla is the unit of magnetic field, see below].
The magnetic field lines form concentric circles around the wire, whose direction is determined by what is known as a " right hand rule ".





Magnetic field at the centre of a circular current loop .

The magnitude of the magnetic field (in a vacuum) B, at the centre of a loop of radius R carrying current, I, is given by



The magnetic field lines are shown in the diagram at left, their direction can be determined by the same right hand rule as above with the thumb now representing the field direction, the fingers representing the current in the loop.


Magnetic field inside a cylindrical solenoid

A solenoid is comprised of multiple current loop wrapped in the form of a cylindrical tube. The magnitude of the magnetic field inside the solenoid with n turns per unit length and carrying current I is given by,

B = µ_oIn
so long as the length of the solenoid is much larger than its diameter. The magnetic field lines are shown in the diagram at right.  Their direction can be determined by a right hand rule with the fingers representing the current flow around the solenoid, the thumb then points in the direction of the magnetic field inside the solenoid.

The magnetic field of a bar magnet and a solenoid have the same structure as shown below,



• The SI unit of magnetic field is the Tesla (T), named for the Serbian/American scientist Nikola Tesla .
  
  1 Tesla = 1 Newton/Ampere.metre
  Also in common use is the Gauss , where 1 Gauss = 10^-4 T.
  The definition of the Tesla in terms of Newtons, Amperes and metres is obtained from the magnetic force law discussed in the next section.
  


• Typical magnitudes of magnetic fields:
• Earth's magnetic field  0.3 gauss


• Bar magnets less than 0.1 T


• Magnetic MRI  scanners, 1-2 T
  
• Inside an atom 14 T  
  

   Supplementary Problems 

Recently, while stopped at a traffic light in the suburbs of Boston with an out-of-state friend, a police car pulled up next to us. On the side was written in large letters: "NEWTON POLICE." My friend's immediate response was, "I wonder what they do. Enforce the Law of Gravity, maybe?"

 

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu