An insulating rod of length L has charge uniformly distributed along its length, as shown in the figure. (a) We have to find the linear charge density of the rod; (b) the electric field at point P a distance a from the end of the rod. (c) If P were very far from the rod compared to L, the rod would look like a point charge. We have to show that our answer for (b) reduces to the electric field of a point charge for

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(a)

As charge is distributed uniformly over length L, the linear charge density will be

.

(b)

Electric field at P due to an infinitesimal length of the rod at a distance x from its far end will be

.

And the electric field at P due to the charged rod will be given by the integral

As the rod is negatively charged, the direction of the electric field will be towards it.

(c)

For , we note that the electric field can be approximated by the expression

.

It is the field due to a point charge.