45.Use Biot-Savart's law to derieve the expression for magnetic field due to circular coil(loop) of radius 'r' having 'n' turns at a point on the axis at a distance 'x' from its centre.

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Q. (a) Write using Biot-Savart law, the expression for the magnetic field

\to B

due to an element

\to d l

carrying current I at a distance

\to r

from it in vector form.
Hence derive the expression for the magnetic field due to a current carrying loop of radius R at a point P distant X from its centre along the axis of the loop.

(b) Explain how Biot-Savart law enables one to express the Ampere's circuital law in the integral form, viz.,

\oint \to B . \to d l = μ_{0} I

Where I is the total current passing through the surface.

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