Calculating Work Required to Move a Charge Between Two Identical Charges

[cashmoney805]

Homework Statement

A +35$$\mu$$C charge is placed 32 cm from an identicle +35$$\mu$$C charge. How much work would be required to move a +.5$$\mu$$C test charge midway between them to a point 12cm closer to either of the charges?

Homework Equations

Wext = -qV
V = kQ/r

The Attempt at a Solution

Q= +35$$\mu$$C, q = +.5$$\mu$$C
I found the initial V, Vi = 2KQ/.16 and then the final V, Vf = KQ[1/.28 +1/.04]
Then I did W = -q(Vf-Vi) and got -2.5J
However, the answer is +2.5 J. This makes sense that the answer is positive- you're moving a + charge from an area of lower to higher potential. Why doesn't this agree with my formula though?

 

[Doc Al]

Why doesn't this agree with my formula though?

Because you are finding the work done by you to move the charge, which is qΔV, not the work done by the field, which is -qΔV.

 

[cashmoney805]

Oh, so Wext = qΔV. So for energy considerations, is it W(by E) + PEi + KEi = PEf + KEf + Wext?

 

[Doc Al]

Oh, so Wext = qΔV.

In this particular case, in which you are moving the charge with the least amount of energy (no excess kinetic energy).

So for energy considerations, is it W(by E) + PEi + KEi = PEf + KEf + Wext?

In general, I would say: PEi + KEi + Wext = PEf + KEf

 

[cashmoney805]

Ok. If another problem asks about W from E, would Wext just be negative in the equation you provided?

 

[Doc Al]

If you want the work done by the electric field, use W = -qΔV.