# Work to move a charge

1. Jan 27, 2009

### cashmoney805

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
Wext = -qV
V = kQ/r

3. 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?

2. Jan 27, 2009

### Staff: Mentor

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.

3. Jan 27, 2009

### cashmoney805

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

4. Jan 27, 2009

### Staff: Mentor

In this particular case, in which you are moving the charge with the least amount of energy (no excess kinetic energy).
In general, I would say: PEi + KEi + Wext = PEf + KEf

5. Jan 27, 2009

### cashmoney805

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

6. Jan 28, 2009

### Staff: Mentor

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