A resistor constructed in the shape of a square prism of length L and sides d is connected across a battery with voltage V as shown in the figure. The resistor's resistivity is not uniform and has the form ?(x) = ?0?(x^2/L^2) along its length using the coordinate system also shown in the figure. Find the charge q contained in the region (1/3)L ? x ? (2/3)L.

 

d d + x = = 0 = (1/3)L x = (2/3)L x = L