A uniform thin rod of length lies along the -axis with its mid-point at the origin

PHYSICS · Subjective · AP · Physics C: Electricity and Magnetism · Electric Charges Fields and Gauss's Law · Electric Charges Fields and Gauss's Law

Problem

A uniform thin rod of length

L

lies along the

x

-axis with its mid-point at the origin. The rod carries a constant linear charge density

\lambda

. (i) Derive an expression for the magnitude of the electrostatic force experienced by a point charge

q

placed on the

x

-axis at a distance

a\,(>\!L/2)

from the centre of the rod. (ii) Show that when

a\gg L

, the expression obtained in part (i) reduces to the result expected for a point charge

q_{\text{eq}}=\lambda L

located at the origin.