# Physics

OUJ Physics Special Course “Time Space and Place Physics” p.15, 16

(Tamiaki YONEYA, Junichiro KISHINE) The force among the Straight Currents are, $$f = \frac{\mu_0}{2\pi}\frac{II_1}{l}$$ $$(I: Test Current, I_1: Current, l: Current Length, \frac{\mu_0}{2\pi}: Decided by the Unit of Current)$$
If we put the Movable Electron’s average vector v, $$I = Ne|\boldsymbol{v}|$$ (N: Numbers of the Conduction Electron per 1 unit of Wire, e: Charge of Electron)

∴ by (1), (2) $$f = \frac{\mu_0}{2\pi}\frac{Ne|{v}|I_1}{l}$$ $$F = \frac{f}{N} = \frac{\mu_0}{2\pi}\frac{e|{v}|I_1}{l}$$ With (2) $$|v| =\frac{I}{Ne}$$ If we put it in (3) $$\frac{f}{N} = \frac{\mu_0}{2\pi}\frac{I}{N}\frac{I_1}{l}$$ $$\frac{I}{N} = \frac{I}{Ne}|q| = |q||v|$$ $$∵ |q| = e, |\boldsymbol{v}| = \frac{I}{Ne}$$ Therefore, by (4) $$F = \frac{f}{N} = \frac{\mu_0}{2\pi}\frac{I}{N}\frac{I_1}{l} = \frac{\mu}{2\pi}|q||v|\frac{I_1}{l}$$ $$F = q\boldsymbol{v}\boldsymbol{B} より \boldsymbol{B} = \frac{F}{q\boldsymbol{v}}$$ from (8), (9), $$|\boldsymbol{B}| = \frac{\mu_0}{2\pi}\frac{I_1}{l}$$