Electric potential in a Uniform electric field

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Jammy4410
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Show that the electric potenital V(r) is a uniform electric field E is given by V(r) = V(0) -E.r

Where E, r and 0 are vectors

So it's a uniform electric field: so the electric field on a charge is the same anywhere in the field and the electric potential is I think given by:

V = - integral of E.dr ?


Not sure what to do from here
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Jammy4410
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so i imagined a positive point charge that (somehow) emits an electric field which is constant in all directions no matter how far away from it/

in this electric field is a positive charge, to move this charge closer to the point charge making the field (from the point r to the point 0) work is done by an external force which is equal and opposite to the electric force i.e

work done = - §eE.dr which is integrated from r to 0 (I've used § in place of an integral sign)

which implies

change in electric potential = -§E.dr

then cause the electric field is constant everywhere, I'm guessing this means something to simplify the integral, like

it doesn't depend on r so can be taken out of the integral like a constant? but its dot product with dr
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Jammy4410
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i got V(0) - V(r) = Er which is wrong, where r = |r|
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Jammy4410
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