Magnetic Forces
Magnetism and Currents
We now move on from examining magnetism on a single charge, to magnetism in relation to multiple moving charges, or currents.
Magnetic Force on a Current
Though it was simplest to define the magnetic field in terms of the force on a
single moving charge, it is nmore common to encounter a current-carrying wire in
the presence of the magnetic field. To find the force on such a wire we simply
need to remember the equation for current:
I = 
, or
that the current is the amount of charge passing through a given point in a
period of time. We may thus substitute
It
for
q
in our equation, our force equation:
F =  =  = 
|
where L is the length of wire with the current running through it. Many times, however, the wire will be very long and we'll want to know the force per unit length. To do so we simply divide both sides of the equation by L :
 = 
|
From this equation we will be able to see many properties of magnetic field.
A Note on Units
Maybe the most confusing thing about electromagnetism is which units are being used at what times. Many texts stick to SI units (meter, coulomb, etc), while others use CGS units (centimeter-gram-seconds). On a theoretical level, it is most convenient to use CGS units, as they make the calculations much simpler, and this text uses this convention. However, since there is a good chance your own text uses SI units, we will provide a conversion table for all the relevant units
| Electric Charge | Coulomb | esu | 1C = 3×109esu |
| Potential | Volt | statvolt | 300V = 1sv |
| Current | Ampere | esu/sec | 1A = 3×109esu/s |
| Magnetic Field | Tesla | Gauss | 1T = 104Gauss |
You shouldn't have to worry about conversions with our problems--only if your own text uses SI units.
