Current Density — Question 5

Question 5

A neutral ionic mixture carries nonzero current

A solution contains number densities n of charges $+2e$ and 2n of charges $-e$. Their drift velocities are $+u\hat x$ and $-3u\hat x$, respectively.

1. Find charge density and current density.

2. Find each species contribution to the current through area A normal to x, and the fraction due to negative ions.

Question 5 - Solution

A neutral ionic mixture carries nonzero current

(a) Method and calculation

$$\rho_q=(+2e)n+(-e)(2n)=0.$$$$\vec J=(2en)u\hat x+(-2en)(-3u\hat x)=8enu\hat x.$$

(b) Interpretation and further calculation

$$I_+=2enuA,\quad I_-=6enuA,\quad I=8enuA.$$$$I_-/I=3/4.$$

Physical check

Charge neutrality concerns signed densities; current also weights those densities by velocity.