Why is there a contradiction in the signs for electrical potential equations?

[x86]

We have two equations

delta EP = -W

V = -Ed

Now, to my understanding for the second equation (E = -V/d) since its a vector quantity, we need to make it have direction

Therefore, if we substitute values E = -50V / 5 m = -10 N/C

We add in the negative sign to the equation because generally:

A proton would move DOWN, therefore the negative sign represents down

-------------------(+)


-------------------(-)

But the confusion stems from the second equation

-------------------(+)
A

B
-------------------(-)

If we have a proton that moves from A to B delta EP would be negative

So -d EP = -W

Work done is positive

But if we move it from point B to A, we exert force on it and therefore work done is negative (according to the equation)

This is extremely weird for me though, because in the first equation we're assuming down is negative and up in positive (like we have been for the rest of the units we've learned)

Yet for the second equation, we assume the exact opposite! Can someone clear up my confusion?

Thanks

 

[sophiecentaur]

There is no contradiction. Electrical potential is defined for a unit Positive charge. The energy for a negative charge would have the opposite sign. To move a proton in a given situation would require equal and opposite work compared with the same operation with an electron. Put the appropriate signs in your equations and the right answer will emerge. Do it for yourself and adhere scrupulously to the signs, without jumping ahead in your mind (which it can be all too easy to do). You will find it works out. No 'verbal' explanation should benecessary.