potential difference=40v b2n plate A & B.

Question

find work done if q=+3C from
a) B to A
b) A to B

*i already know the ans but i need the explanation for the formula.

-this is my work
a)w=-qv b)-120J
=-3(-40)
=120 J

what i want to ask is:
1-why must we add - sign for v is not that if the v is against electric field is +?

Answer 1

You don't say whether A or B has the higher potential. You only say that the difference "between" them is 40 V.

If a positive charge moves to a higher potential, the potential energy increases. The E field and force is opposite to the direction of motion in that situation.

Answer 2

i'm sorry. the electric field are from A to B.

dear drwls,you didn't answer my question.
i know about the concept but why the v is negative? or how can it be proven mathematically by the formula?.

Answer 3

Start with the definition of work
Work=Force dot distance
= Eq dot distance
but E=-dV/dx by definition of direction of E field. E goes from + V to -V (the direction of a pos test charge)
Work= q*-dV/dx dot distance
work= -q dV/dx dot dx


Now, if the distance is in the direction of the gradient, then
work=-q DeltaV