A charged nonconducting rod, with a length of $2.00 \mathrm{~m}$ and a cross-sectional area of $4.00 \mathrm{~cm}^2$, lies along the positive side of an $x$ axis with one end at the origin. The volume charge density $\rho$ is charge per unit volume in coulombs per cubic meter. How many excess electrons are on the rod if $\rho$ is uniform, with a value of $-4.00 \mu \mathrm{C} / \mathrm{m}^3$?

$2.00 \times 10^{10} \text { electrons; }$