How Many Excess Electrons Are on a Charged Rod with Nonuniform Density?

[Jrlinton]

Homework Statement

A charged nonconducting rod, with a length of 1.33 m and a cross-sectional area of 3.40 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 -4.22 µC/m3, and (b) nonuniform, with a value given by ρ = bx2, where b = -2.66 µC/m5?

Homework Equations

q=ne
p=bx^2

The Attempt at a Solution

So for part a:
n=(p(a)L)/e
n=(-4.22E-6C)(3.4E-4m^2)(1.33m)/(-1.6E-19C)
n=1.193E10 electrons

Part b is where i was incorrect
p=bx^2
p=-2.66x^2
dq=Apdx
=3.4E-4*-2.66x^2dx
so q=9.04E-4* the integral of x^2dx from 0 to 1.33
q=-7.09E-4C
n=q/e
=-7.09E-4C/-1.6E-19C
=4.431E15 electrons<----- this was incorrect and I am unsure of my mistake

 

[gneill]

Part b is where i was incorrect
p=bx^2
p=-2.66x^2
dq=Apdx
=3.4E-4*-2.66x^2dx
so q=9.04E-4* the integral of x^2dx from 0 to 1.33 ⇐
q=-7.09E-4C
n=q/e
=-7.09E-4C/-1.6E-19C
=4.431E15 electrons<----- this was incorrect and I am unsure of my mistake

Looks like the order of magnitude went astray starting here. 10^-4 is too big. Check the units of the constant b.

 

[Jrlinton]

Right, so multiply the final answer by the conversion factor of microcoulombs to coulombs of E-6.

 

[gneill]

That'll work.