Question

Derive means prove

(a) Using the result of the magnetic fi conductor: ? 401/ 217, derive the Force between parallel conductors. Hint: Follow the lecture in class] (b) Using the expression you have just derived in part (a), define "Ampere", the SI unit of current

Answer 1

5.

(a)

$\vec F_2 =I_2\vec L_2 \times \vec B_1$

$B_1=\frac {\mu_0 I_1}{2\pi r}$

$F_2=\frac {I_2L_2\mu_0I_1}{2\pi r}$

$\frac {F_2}{L_2}=\frac {\mu_0}{4\pi}\frac {2I_1I_2}{r}$

$f=\frac {\mu_0}{4\pi}\frac {2I_1I_2}{r}$ ( f : Force per unit length)

(b)

1 Ampere is that amount of current which when flowing in two parallel wires, placed at a distance of 1 m in the vacuum, produces a force equal to  $2\times 10^{-7}\: N$ per meter of length.