# Magnetic field on an arbitrary point ON a Current Loop

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.

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.

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.