A rod of length ? with uniform charge per unit length ? , where ? > 0, is placed

Question

A rod of length ? with uniform charge per unit length ? , where ? > 0, is placed a distance d from the origin along the x axis. A similar rod with the same charge is placed along the y axis as in the figure. Consider only a small segment of length ? x (it is of infinitesimal length) on the horizontal rod, which is placed along the x axis. The segment is at a distance x from the origin,Determine the electric field ?E at the origin due to this segment. Determine the electric field ~ E rod1 at the origin due to the entire horizontal rod.Determine the electric field ~ E tot at the origin due to both rods.

Explanation / Answer

1.

From the fact that ? > 0 and the diagram,
the field ?E at O due to the segment on the
x-axis is in the negative x direction, and its
magnitude is given by

2.

For the entire rod, we must add all the
segments, i.e., integrate from x = d to x =d + ?. The electric field due to the horizontal rod is

3.

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