Question

State Biot-Savart's law? Define the unit of current.

Answer 1

Let $AB$ is a conductor carrying current $i$. Consider a small element $dl$ length of the conductor, due to this the magnetic field $dB$ is produced at a point $P$ distance $r$ from $dl$, $\theta$ is angle by $dl$ to point $P$, then the intensity of field $dB$ is:
(1) Directly proportional to the current $i$ $dB\propto i$.
(2) Directly proportional to the length of the conductor $dB\propto dl$.
(3) Directly proportional to the sine of the angle between the line joining the point and $dl$ $dB\propto \sin \theta$.
(4) Inversely proportional to the square of the distance of the point $P$ from the line $dB\propto \frac{1}{r^2}$. Combining all the four
$dB\propto \frac{idl\sin \theta }{r^2}$
$dB=k\frac{idl\sin \theta }{r^2}$ $k$ is constant
$k=\frac{{\mu }_0}{4\pi }={10}^{-7}N/A^2$
$dB=\frac{{\mu }_0}{4\pi }\frac{idl\sin \theta }{r^2}={10}^{-7}\frac{idl\sin \theta }{r^2}Wb/m^2$
In above formula $dl=1m$, $\sin \theta =1$, $\theta =90$
$r=1m$; $dB={10}^{-7}Wb/m$
$i=1$ Ampere
Hence one ampere current is that current which produces a field of ${10}^{-7}Wb/m^2$ at the centre of a conductor of length $1m$ placed in the form of an arc of a circle of radius $1m$.