Question

State Biot-Savart's law. Define 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

$dB\propto \frac{idlsin\theta }{r^2}$

$dB=k\frac{idlsin\theta }{r^2}k$ is constant

$k=\frac{{\mu }_0}{4\pi }={10}^{-7}N/A^2$

$dB=\frac{{\mu }_0}{4\pi }\frac{idlsin\theta }{r^2}={10}^{-7}\frac{idlsin\theta }{r^2}Wb/m^2$

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 1 m placed in the form of an arc of a circle of radius 1 m.