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Consider this situation given above. We have an arbitrarily shaped theoretical current loop made up of wire of zero radius in free space. Away from all electromagnetic, gravitational interactions.

Meaning, THERE IS NO EXTERNAL FORCE ON THE CURRENT LOOP SYSTEM.

Now consider an infinitesimal current element vector $idl$ at point A, like so.

enter image description here If we consider the magnetic field at A = $B$(A)

To determine the magnetic field at that point, let us split our work into two...

DIRECTION OF $B$(A)

The direction of the Magnetic field will NOT be in the plane of the loop, as this will accelerate the body Either linearly or increase its angular acceleration. Also, the Magnetic field cannot be parallel to the loop as then it contradicts the Ampere circuital Law as:

$$Σ_(0 to L)Bdl=μ_0i=0$$ therefore $B$ along the wire is zero.

Clearly, if there is any Magnetic field on the loop it must be perpendicular to the loop.

MAGNITUDE OF THE MAGNETIC FIELD

Now according to Newton's II Law, the Net force on that isolated current loop is ZERO.

So,$$Σ(0 to L)Bidl=0$$ Since i, L are not zero, the net Magnetic field on any point of the loop is zero.

MY QUESTION IS THIS

Imagine we remove the infinitesimal current element at A and take infinitely away from the setup.

enter image description here

Since the magnetic field at A due to the Current element at A was infinite (undefined) initially, The magnetic field due to the rest of the loop at A must also be exactly that infinity.

AM I RIGHT? KINDLY DO CORRECT ME IF GOOFED UP SOMEWHERE.

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The magnetic field at A due to the infinitesimal element is not infinite...This can be thought to be analogous to the electric field just outside a charged plane...The thing I want to say is that the field due to an infinitesimal element at infinitesimal distance can be finite...

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  • $\begingroup$ In the real world, the only way to get an infinite field from a current in a wire is if the wire has a radius of zero. $\endgroup$ – R.W. Bird Apr 25 at 19:11
  • $\begingroup$ @R.W. Bird, I was talking about this as a theoretical possibility... $\endgroup$ – JjJot Apr 26 at 5:00
  • $\begingroup$ @user89505, I think that theoretically, an infinitesimal current element can have an infinite magnetic field. See en.wikipedia.org/wiki/Biot%E2%80%93Savart_law. $\endgroup$ – JjJot Apr 26 at 8:09
  • $\begingroup$ In either case, the contributions from current segments which are a finite distance away from the one in question would not be infinite. $\endgroup$ – R.W. Bird Apr 26 at 18:01

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