$ \Delta\varphi = R I $

Dphi = R * I

$ v_{max} =\displaystyle\frac{ e E }{ m_e } \tau $

v_max =( e * E/ m_e )* tau

$ I =\displaystyle\frac{ e ^2 E }{2 m_e } \tau c S $

I = e ^2* E * tau * c * S /(2* m_e )

$ E =\displaystyle\frac{ \Delta\varphi }{ L }$

E = Dphi / L

$ \Delta\varphi =\displaystyle\frac{2 m_e }{ e ^2 \tau c }\displaystyle\frac{ L }{ S } I $

Dphi =(2 * m_e /( e ^2* tau * c ))*( L / S )* I

$ \rho_e =\displaystyle\frac{2 m_e }{ e ^2 \tau c }$

rho_e =2* m_e /( e ^2* tau * c )

$ R = \rho_e \displaystyle\frac{ L }{ S }$

R = rho_e * L / S

$ a =\displaystyle\frac{ e E }{ m_e }$

a = e * E / m_e

$ I = e S c \bar{v} $

I = e * S * c * v_m

$ I =\displaystyle\frac{ \Delta Q }{ \Delta t }$

I = DQ / Dt

$ v_{max} = a \tau $

v_max = a * tau

$ \overline{v} =\displaystyle\frac{1}{2} v_{max} $

v_m = v_max / 2