Calculating Work Required to Move a Charge Between Two Identical Charges

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To calculate the work required to move a +0.5μC test charge between two +35μC charges, the initial and final electric potentials were determined using the formula V = kQ/r. The initial potential was calculated as Vi = 2KQ/0.16, while the final potential was Vf = KQ[1/0.28 + 1/0.04]. The work done by an external force was found using W = -q(Vf - Vi), resulting in -2.5J, but the correct interpretation shows that the work required is +2.5J, as moving a positive charge from lower to higher potential requires energy input. The distinction between work done by the external force and work done by the electric field is clarified, emphasizing that Wext = qΔV for external work. This discussion highlights the importance of understanding potential energy changes in electrostatics.
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Homework Statement


A +35\muC charge is placed 32 cm from an identicle +35\muC charge. How much work would be required to move a +.5\muC 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\muC, q = +.5\muC
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?
 
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cashmoney805 said:
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.
 
Oh, so Wext = qΔV. So for energy considerations, is it W(by E) + PEi + KEi = PEf + KEf + Wext?
 
cashmoney805 said:
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
 
Ok. If another problem asks about W from E, would Wext just be negative in the equation you provided?
 
If you want the work done by the electric field, use W = -qΔV.
 
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