Question

A very long, straight, then wires carries $-3.60nC$ $m^{-1}$ of fixed negative charge. The wire is to be surrounded by a uniform cylinder of positive charge, radius $1.50cm$, coaxial with the wire. The volume charge density $\rho$ of the cylinder is to be selected so that the net electric field outside the cylinder is zero. Calculate the required positive charge density $\rho$ (in $\mu C$ $m^{-3}$)

• A. $6$
• B. $7$
• C. $5$
• D. $3$

Answer 1

Answer: (C)

$5$

We don't really need to write an integral, we just need the charge per unit length in the cylinder to be equal to zero. This means that the positive charge in cylinder must be $+3.60nC{m}^{-1}$. This positive charge is uniformly distributed in a circle of radius $R=1.50cm$, so
$\rho =\frac{3.60nC{m}^{-1}}{\pi {\left(0.015m\right)}^2}=5\mu C{m}^{-3}$