(a) Write using Biot-Savart law, the expression for the magnetic field →B due to an element →dl carrying current I at a distance →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., ∮→B.→dl=μ0I Where I is the total current passing through the surface.

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

1.	(a) Write using Biot-Savart law, the expression for the magnetic field →B due to an element →dl carrying current I at a distance →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., ∮→B.→dl=μ0I Where I is the total current passing through the surface.
Answer» (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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