The compass doesn’t give you the value of the net magnetic field, just the direction. So, how do you get the magnitude of a particular field from this? The trick is to assume the value of the Earth’s magnetic field and the direction of the compass. Let’s assume that at this location on the Earth, the magnetic field is pointing directly North with a horizontal component of about 2 x 10-5 T.
Now suppose that I do something to create a magnetic field in a known direction and perpendicular to the horizontal component of the Earth’s magnetic field. Here is an example where I put a current carrying wire right over the compass needle. Since the compass is underneath the wire, the magnetic field due to the wire will be 90° to the Earth’s magnetic field.
