Question

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

The limits of the integration will be $\mathbf{-}\mathit{L}\mathbf{/}\mathbf{2}$to$\mathbf{+}\mathit{L}\mathbf{/}\mathbf{2}$.

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$dx$ with a charge$\lambda dx$ where$\lambda$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 $+L/2$.