Q.Write down the vector form of Biot-Savart's law. Using this law, derive an expression for the magnetic field at the centre of a circular coil carrying current. (1+2) OR A galvanometer of resistance 100 Ω gives full scale deflection for a current of 1 mA. How will you convert it into

Integrating the Biot–Savart law's contribution from every current element around a circular loop gives the well-known result B = μ₀I/2R at the centre.

Biot–Savart law (vector form): the magnetic field $d\vec B$ at a point due to a small current element $I\,d\vec l$, at a position vector $\vec r$ (unit vector $\hat r$, distance $r$) from the element, is:

$d\vec B = \dfrac{\mu_0}{4\pi}\ \dfrac{I\,d\vec l \times \hat r}{r^2}$

where $\mu_0$ is the permeability of free space. Its direction is given by the right-hand (or Fleming's) rule, perpendicular to both $d\vec l$ and $\hat r$.

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