is not the "tot. charge", it is the charge at a single point. It's been a few years since I took calculus (so maybe someone else can correct me if I'm mistaken), but I believe you need to calculate:
I have a cylinder whose radius, r = a & length = L
charge distribution through cylinder is
ρ = C/2 * r^{3}
where r = radial distance in cylindrical coordinates
C = constant
show that the average charge density ρbar = Ca^{3} / 5
* * * * * * * * * * * * *
I have average charge = tot. charge / tot. volume
aAGH! Amendment
vol = ∏r^{2}L
i.e. ρ / ∏r2L
= ((C/2)*r^{3}) / ∏r^{2}L
= Cr^{3} / 2∏r^{2}L
= Cr / 2∏L
= Cr^{2} / 6.28L
Now this should make more sense to me but doesn't.
is not the "tot. charge", it is the charge at a single point. It's been a few years since I took calculus (so maybe someone else can correct me if I'm mistaken), but I believe you need to calculate: