Astraight wire of length l has a positive charge q distributed along its length. find the magnitude of the electric field due to the wire at a point located a distance d from one end of the wire along the line extending from the wire. imagine that distance d is much greater than the length of the wire. intuitively, what should the magnitude of the electric field at point p be in this case

Electric Field at a distance d from one end of the wire is

Electric Field when d is much grater than length of the wire =

Explanation:

Given:

Let dE be the Electric Field due to the small elemental charge on the wire at a distance x from the one end of the wire and let be the charge density of the wire

Now integrating it over the entire length varying x from x=d to x=d+L we have and replacing we have

When d is much greater than the length of the wire then we have

1+\dfrac{L]{d}≈1

So the Magnitude of the Electric Field at point P =

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