# If there are no poles in the magnetic field around the wire, why is the compass pointer deflected?

If in a straight wire, current flows, and magnetic field is created there are no poles to it. Then why does a compass brought near it gets deflected if there are no poles? if the direction of the magnetic field affects the pointing of the poles then please explain how it affects ?

## 2 Answers

It is neither necessary nor useful to look for poles in the magnetic field of the wire, since its field lines are circles around the wire, so they don't have a dipolar structure.

The needle of the compass, however, is a magnetic dipole. As such, it gets a potentiel energy when it's inside a magnetic field: $$V=-\vec{\mu}.\vec{B}$$ with $$\vec{\mu}$$ is the dipole moment of the needle and $$\vec{B}$$ the magnetic field coming from the wire.

This expression is smallest (stable equilibrium) or highest (unstable equilibrium) when both vectors are aligned, which means that the field can make the needle turn.

If necessary, you can also see it with the torque applied by the field to the needle: $$\vec{\Gamma}=\vec{\mu}\times\vec{B}$$ Again, this shows that a torque is applied until the needle is aligned with the field.

The magnetic field around conductor having a current is having relativistic poles.

Meaning; if you select a point in the field it will be north pole to the point before it and at the same time it is a south pole to another point after it.