# (a) State and explain the law used to determine magnetic field at a point due to a current element. Derive the expression for the magnetic field due to a circular current carrying loop of radius r at its centre.(b) A long wire with a small current element of length 1 cm is placed at the origin and carries a current of 10 A along the X-axis. Find out the magnitude and direction of the magnetic field due to the element on the Y-axis at a distance 0·5 m from it.

Biot-Savart's Law: Determines the magnetic field at any point due to current-carrying conductor.

According to Biot-Savart law,  the magnetic field at a point P which is at a distance r from the current element is given by

Consider a circular loop of radius r and a small current element dl, then the magnetic field due to the current element at the centre o of the circle is given by

Total magnetic field

(b) Given:  A length of wire - 1 cm

current carry =10A

Now, the direction of  magnetic fields:

in z-direction

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