Find change in electric potential energy

[sunset117]

Homework Statement

A uniform electric field of magnitude 4.1 ✕ 10^5 N/C points in the positive x-direction. Find the change in electric potential energy of a +5.3 µC charge as it moves from the origin to each of the points given below.
(a) (0, 6.9 m)
__ J

(b) (6.9 m, 0)
__J

(c) (6.9 m, 6.9 m)
__J

Homework Equations

I'm confused by the phrase electric potential energy. I was thinking I should use V= k|q|/r^2 but was then confused. Electric potential is V=kq/r so should I maybe just do that for an initial and final on each? Some research made it sound like I would use ( ∆V = -E*∆s ). Can someone help me as to which direction I should go?

The Attempt at a Solution

 

[Delta2]

The correct direction is towards the use of formula $\Delta V=-E\Delta s$ because the other formula you mention (V=Kq/r) is for the potential energy of the charge due to the field that charge itself creates . But here we are asked for the potential energy due to the external electric field.

However you need to be careful on the use of $\Delta V=-E\Delta s$ because it is in an oversimplified form. The correct form of the formula has dot product and not simple scalar product (and also the use of integral in front of the product).

To give an additional tip, the answer for b) and c) is the same but the answer for a) is different.