Charge and excess electrons in a rod

[nothingatall]

Homework Statement

A charged nonconducting rod, with a length of 3.00 m and a cross-sectional area of 5.37 cm2, lies along the positive side of an x-axis with one end at the origin. The volume charge density ρ is charge per unit volume in coulombs per cubic meter. How many excess electrons are on the rod if ρ is (a) uniform, with a value of -2.54 µC/m3, and (b) nonuniform, with a value given by ρ = bx2, where b = -1.36 µC/m5?

Homework Equations

F=kQq/r^2
q=volume charge density*area of circle*length

The Attempt at a Solution

q=p*(pi)r^2*L=-2.54e-6C/m^3*5.37cm^2*3.00m=-4.09e-9
q/e=-4.09e-9/-1.6e-19=2.6e10e<--this was correct

part b: p=bx^2=-1.36e-6x^2
dq=Apdx
dq=5.37e-4*-1.36e-6x^2 dx
did the integral procedure and it may be wrong:
integral(dq)=7.3032e-10 *integral (x^2) from 0 to 2 =-1.94e-9
q/e=-1.94e-9/-1.6e-19 = 1.22e10<-- marked incorrect

I don't know how to fix this.

 

[ideasrule]

Why did to integrate from 0 to 2 if the length of the rod is 3 m?

 

[nothingatall]

I was practicing the example from the book and mistakenly used that value haha... Thanks!