Consider a small piece of wire of length ds carrying a current I. This defines a vector **ds** that points in the direction of the current. The magnetic field **dB** set up by this piece of current-carrying wire at a point a distance r away is:

All of these observations can be satisfied by the equation:

**dB** = (m_{o} / 4p ) I **ds** ´
/r^{2}

where the constant m_{o} is known as the permeability of free space and has a value of

m_{o} = 4p x 10^{-7} T m /A

Compare the result for **dB** to the electric field **dE** we get from a point charge dq:

**dE** = ( 1 / 4p e_{o} ) dq
/r^{2}

To find the total field at a point from an entire wire, simply integrate all the **dB**'s:

Net magnetic field is **B** = ( m_{o} I / 4p ) ò **ds** ´
/r^{2}

The process is very similar to what we did to find electric field from charge distributions.