A “semi-infinite” insulating rod carries a constant charge per unit length of . We have to show that the electric field at the point P makes an angle of with the rod and that this result is independent of the distance R.

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We will calculate the x-component and the y-component of the field at the point P, as shown in the figure, due to the “semi-infinite” insulating rod carrying uniform linear charge of density .

Consider an infinitesimal charge element of length at distance x from the end of the rod as shown in the figure.

As the direction of electric field due to a charge element is along the line joining the element to the point where field is to be calculated, the x-component of the field will be

Integrating over the length of the “semi-infinite” rod that is with respect to the variable x from , we get

Similarly,

And

For calculating this integral, we make the substitution

We have

We note that

for all R.

Therefore, the angle that the electric field vector makes at P is

.

It implies that and is independent of R that is the distance of the point P from the edge of the “semi-infinite” rod.