Ampere’s law

We know that a straight conductor creates a circular magnetic field. The direction of the magnetic field, B, at a given point is simply the tangent to that circle. The magnitude is given by Ampere’s law:


where B is the magnetic field in teslas (T), μ0 is the permeability of free space (it has a constant value of 4π × 10−7 T⋅m/A), and r is the distance from the conductor in metres (m).

For a coiled conductor (a solenoid), we use the equation


where B, μ0, and I are the same as before, and where N is the number of loops (unitless; always an integer; counted number, therefore significant digits; if you are solving for it, round up, never down) and L is the length of the solenoid in metres (m).


Find the magnitude of the magnetic field 3.2 cm from a straight conductor with 0.75 A of current.

All we have to do is plug everything into the equation:

|B|=(4π×107 T⋅m/A)0.75 A2π(0.032 m)4.6875×106 T.

Therefore, the magnitude of the magnetic field is 4.7 × 10−6 T.