# 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

Unit SI Unit CGS Unit Conversion
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.

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