Derive an expression for the magnetic field at a point on the axis of a current carrying circular coil. Also find the magnetic field at the centre of the coil.

**OR**

Find the force acting on a current carrying conductor in a uniform magnetic field. Using it find the force betw

Question

Derive an expression for the magnetic field at a point on the axis of a current carrying circular coil. Also find the magnetic field at the centre of the coil.

**OR**

Find the force acting on a current carrying conductor in a uniform magnetic field. Using it find the force between two parallel current carrying conductors.

Accepted Answer

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> [!TLDR]
> Applying the Biot-Savart law to every current element around the loop and using symmetry to cancel the perpendicular field components leaves only the axial component, which integrates to a clean closed-form expression for B(x); setting x=0 gives the field at the centre.
>
> **Setup:** Consider a circular coil of radius $R$ carrying current $I$, and a point $P$ on its axis at a distance $x$ from the centre $O$. Consider a small current element $Idl$ on the coil; the distance from this element to point $P$ is $r = \sqrt{R^2+x^2}$.
> …

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