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Consider I have a finite line of charge.If I find the electric field at a point near the centre of the line charge the net field is horizontal as the vertical component get cancelled.If I find the electric field at a point slightly towards the ends of the line charge I get a horizontal and vertical component.Now say I have an infinite line charge, the net electric field I find at any point will be horizontal or radial as the vertical components get cancelled. Here is my real confusion.My professor said that if the distance is very less compared to the dimensions of the distribution,the distribution will appear to be infinitely large.Now if I find the electric field at a point very very close to a FINITE line charge, at that point the electric field vector should be radial or horizontal because from that point it appears to be an infinite line charge and in an infinite line charge net electric field vector must be radial but logically and practically since it is still a finite line charge and I am finding the net field at a point near the ends,shouldn't there be a horizontal and vertical component and not just a radial component?What am I getting wrong?Can someone explain this clearly?

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  • $\begingroup$ There would be a component other than a radial component, at any point other than at the center. However at the ends,if you get close to the line, the DOMINATING contribution is just the charge directly below it, this charge only gives a radial component. The other contributions to the field from the other parts of the wire are small. So can be APPROXIMATED as such. In reality, it will not just have a radial component. $\endgroup$ May 13, 2022 at 17:43
  • $\begingroup$ I would also believe that if you get infinitely.close to it, it will approach a purely radial component,however the field is infinite. $\endgroup$ May 13, 2022 at 17:45
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    $\begingroup$ Protip: if you don't want to come off as an absolute nutjob, try putting a space after the period when you start a new sentence. $\endgroup$
    – hft
    May 13, 2022 at 18:00
  • $\begingroup$ That comment was mostly directed at OP :) $\endgroup$
    – hft
    May 13, 2022 at 22:41
  • $\begingroup$ I am sorry for not putting the space. I will be careful next time. So according to the answers I've got the radial component becomes more dominant as we get closer and closer to the finite line charge? $\endgroup$
    – AJknight
    May 14, 2022 at 4:12

2 Answers 2

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Note that on the surface of the line that produces the finite line charge, the electric field lines must exit normal to that surface. This means that for any point that is sufficiently close to that surface, the electric field will indeed look like it is emanating from an infinitely long line.

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It's an approximation. The field is almost radial if:

l/r >> 1

and

x/r >> 1

where

l is the length of the line. r is the radial distance from the line. x is the distance to the nearest end of the wire.

For a more practical case, take r to be the radius of a wire. You've just dipped your toe into antenna theory.

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