Nonuniform charge density

Question

A 37.4 cm long rod has a nonuniform charge density given by the equation

λ(x)=A(1-x/b)²

where A = 5.00 nC/cm and b = 26.4 cm. What is the total charge on the rod?

Answer 1

The conceptual key is that the total charge is the integral over the charge density. This is because the charge density tells you the amount of charge per each infinitesimal piece, and the integration just adds those all up.

Therefore, all you have to do is evaluate the definite integral of the charge density over x, from x=0 to x=37.4.

The result is the total charge!

Hope this helps,

Sam