Question

Derive the formula $\frac{F}{l}=\frac{{\mu }_o}{2\pi }\cdot \frac{i_1{i}_2}{r}$ as the force per unit length between two parallel wires each of length l meter, carrying currents $i_1$ and $i_2$ amperes and separated by a distance r meters. Define ampere with the help of this formula.

Answer 1

Field at wire 2 is $B_1$

$B_1=\frac{{\mu }_o{i}_1}{2\pi r}$

Force on 2nd wire is f

$f=i_{2}lB\sin g{0}^{\circ }=\frac{{i_{2}l\mu }_o{i}_1}{2\pi r}$

$\frac{f}{l}=\frac{{\mu }_o{i}_1{i}_2}{2\pi r}$

If $i_1=i_2=1Aandr=1m$

$\frac{f}{l}=\frac{{\mu }_o{i}_1{i}_2}{2\pi r}=2\times {10}^{-7}N{m}^{-1}$

If two parallel wire separated by distance r = 1 m, and carry current .

Such that the force of attraction between then is $2\times {10}^{-7}N{m}^{-1}$. Then the amount of current in each wire is said to be 1 ampere.