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@Samyak-Sharma
The drift velocity, U=I/NAQ . The Current I , Charge Density N , and the Charge magnitude Q is constant. The only variable is the area. Let the length along the axis be z with z=0 at the first face. The area A could be then written as (y+yz)(2x-xz) = xy(1+z)(2-z). Here, x and y are constants and the variable is z . Differentiating (1+z)(2-z) w.r.t z and equating to 0 we get the maxima at z=0.5 . Thus, the area is maximum at z=0.5 and the drift velocity U is therefore minimum at z=0.5 .