Chapter 15: Q1Q (page 616)

Consider setting up an integral to find an algebraic expression for the electric field of a uniformly charged rod of length L , at a location on the midplane. If we choose an origin at the center of the rod, what are the limits of integration?

Short Answer

Expert verified

The limits of the integration will be $- L / 2$ to $+ L / 2$ .

Step by step solution

Given data

A uniformly charged rod of length $L$ .

Step 2:Integration to find the electric field

The net electric field due to a uniform charge distribution is obtained by first calculating the electric field due to a small charge element in the distribution and then integrating it over the whole distribution.

Step 3:Determining the integration limit to find the electric field due to a uniformly charged rod on its midplane

To obtain the field due to the rod on its midplane, at first, the field due to a small length element $d x$ with a charge $λ d x$ where $λ$ is the charge per unit length is obtained. Here the $x$ axis is chosen along the rod with the mid-point at the origin.

Thus the integration to find the electric field due to the whole rod will be carried out fromrole="math" localid="1668498796461" $- L / 2$ to $+ L / 2$ .