Give differences between Biot-Savart law and Coulomb’s law.

A long straight wire, carrying current $I$ is bent at its mid-point to form an angle of $45^{\circ}$. Induction of magnetic field (in tesla) at point $P$, distant $R$ from point of bending is equal to

A Helmholtz coil has pair of loops, each with $N$ turns and radius $R$. They are placed coaxially at distance $R$ and the same current $I$ flows through the loops in the same direction. The magnitude of magnetic field at $P$, midway between the centres $A$ and $C$, is given by (Refer to figure)

The fractional change in the magnetic field intensity at a distance $'r'$ from centre on the axis of current carrying coil of radius $'a'$ to the magnetic field intensity at the centre of the same coil is : (Take $r << a )$

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point $P$ which lies on the centre of the semicircle ?

A wire carrying $I$ is shaped as shown. Section $AB$ is a quarter circle of radius $r.$ The magnetic field at $C$ is directed