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## Homework Statement

I have two problems, both using different equations for electric potential. Confused on when to use which.

First problem:

Two parallel plates connected by a battery whose electric potential is 12V. One plate Has charge density σ

^{+}and the other has Charge density σ

^{+}. The plates are spaced 3x10

^{-3}m. We want to find the electric field. The way the problem is solved:

ΔV=U/q

U=qEd

Combining the two above:

ΔV=Ed→E=ΔV/d→E=12V/(3x10

^{-3}m)=4x10

^{3}V

The next problem wants to know the electric potential energy of moving a proton like the attached picture.

It is solved like this:

ΔV=-Ed=-(8x10

^{4}V/m)(0.5m)=-4x10

^{4}V

Then:

ΔU=qΔV=(1.602x10

^{-19}C)(-4x10

^{4}V)=-6.4x10

^{-15}J

My question:

Why I’m the first problem did we say ΔV=Ed

And in the second problem

ΔV=-Ed?

Thanks!