What is the electric force on the plastic stirrer if the end closest to the wire is 2.0 cm away?

Question

Your physics assignment is to figure out a way to use electricity to launch a small 6.0-cm-long plastic drink stirrer. You decide that you'll charge the little plastic rod by rubbing it with fur, then hold it near a long, charged wire. When you let go, the electric force of the wire on the plastic rod will shoot it away. Suppose you can charge the plastic stirrer to 13.0 nC and that the linear charge density of the long wire is 1.0*10^-7 C/m

What is the electric force on the plastic stirrer if the end closest to the wire is 2.0 cm away?

Answer 1

E = 2kλ/r    (field strength of long line of charge)

F = qE = 2kλq/L*∫dr/r = 2kλq/L*∫dr/r

    integrate from .02 to .02 + L

= 2kλq/.06*(ln.08 - ln.02) = 5.40e-4 N