Why is the magnetic field around a straight current-carrying wire in concentric cirlces?

Question

I have a question that, why are the magnetic field lines around a straight current carrying wire in the form of concentric circles?

If the wire is carrying current, it is acting like a magnet. So shouldn't the magnetic field resemble the magnetic field created by a bar magnet? Then why is it in the form of concentric circle and not the oval-shaped circles as seen in a bar magnet? Magnetic Field around a bar magnet1

@Newbie I'm curious — why would the length of the wire matter? — Shane, Jan 15 '22 at 08:34
@Newbie length doesn't matter at all just it will contribute in increasing or decreasing the $STRENGTH$ of the magnetic field at some point. the magnetic field lines will still be in the circular shape as it was before. — Tejas Dahake, Jan 15 '22 at 08:58
Try completing the field lines for the magnet with the parts inside the magnet. You will find they are loops. The permanent magnet acts as if it had a current flowing around it, not from N to S but in the direction around the body, on its surface. — Andrew Steane, Jan 15 '22 at 09:50
Related : A generalization of the Biot-Savart law for a number n of wires with n≥3. — Frobenius, Jan 15 '22 at 10:59
@TejasDahake By length being unrealistically set to infinity we essentially don’t have a closed loop of static current. Compare it to the field lines of a closed loop current, i.e, a dipole. This was the point I was trying to make. — Newbie, Jan 15 '22 at 12:06

Tejas Dahake · Answer 1 · 2022-01-15T09:16:27.627

They form circular in shape because it tells us that the magnetic field is constant in this circular path.

Since according to the Biot-Savart law the magnetic field strenght is inversely proportional to the square of distance and we have to define the same magnetic strength at a different point and that is only possible if the magnetic field lines are circular that means the magnetic field is constant but on the different point in the space. just in case if it was not constant then it will be formed in the oval shape or any other uneven shape as you said in the case of the bar magnet. otherwise magnetic field is every where in the space and the magnetic field lines only tells us in which direction the magnetic fields are going to be made at some point.

That's why they are circular in the shape.

score 0 · Answer 2 · answered Jan 15 '22 at 08:31

Let's assume that the wire here is very long and very straight. There is a nice argument based on symmetry which suggests that the magnetic field around the wire have to be concentric circles.

Let us suppose that the magnetic field were not concentric circles, but concentric squares or "off centre" circles. Now, we rotate the wire along its axis by a few degrees. Since the wire rotates, the orientation of the magnetic field in space should also change, right?

But, we can also argue that the magnetic field should not change, because the appearance of the wire has not changed. Two perfectly logical and valid lines of reasoning have produced contradictory results!

The only way to resolve this contradiction is to postulate that the magnetic field around the long, straight wire form concentric circles.

The bar magnet does not have the rotational symmetry of a long, straight wire, so the above reasoning will not apply to it.

score 0 · Answer 3 · answered Apr 06 '22 at 07:02

The field of the bar magnet is essentially the same of a current-carrying wire with a circle shape. A straight wire give a field of concentric circles. If you transform the straight line into a circle, a ring-wire, the concentric circles transform in the bar magnet pattern.

Why is the magnetic field around a straight current-carrying wire in concentric cirlces?

3 Answers3