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I seem to have trouble understanding this. The way I understand it leads to an inconsistency, so there must be something I'm not getting. Please forgive me if my explanation is unclear.

The potential difference between two points (say A and B) in an electric field is:

-[integral from A to B]E. ds

Ifsis parallel toE, then it becomes -Es

where s is the distance between the two points.

The potential difference between two points in the electric field of a point charge q is:

(Ke)q * [ (1/rB) - (1/rA) ]

where rB and rA are the distances between the respective point and q.

Now, usually we chose V = 0 at rA = (infinty), thus the equation becomes:

(Ke)q / rB

However, when we consider two points A and B to be in line with a point charge q, if we let rA = (infinity) then the distance s between A and B is (infinty).

The equation (Ke)q * [ (1/rB) - (1/rA) ] still appears fine, but what about -Es ? The situation seems to fit for that equation becausesis parallel to the field line coming from the point charge. However, we end up with -E(infinity) .

This means that:

-E(infinity) = (Ke)q / rB

(infinity) = (Ke)q / rB

Which means that q must be infinite.

There's got to be something wrong with my reasoning, can someone please tell me what it is?

Thanks,

Dale

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# Homework Help: Voltage in electric field

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