find the net current flowing out of the battery and potential at B.

Answer

`((sqrt5 - 1)/(2))`

Explanation

`vec(y) = ((rhol^(2)) xx (l)/(2) - (rhoa^(2))(a)/(2))/(rhol^(2) - rhoa^(2)) = a rArr l^(2) - al - a^(2) = 0`
`rArr a = ((sqrt5 - 1)l)/(2) x`