How Much Work is Needed to Bring Two Point Charges Together?

[rbraunberger]

Homework Statement

Two point charges Q1 = 3.3 µC and Q2 = 7.6 µC are initially very far apart. They are then brought together, with a final separation of 2.6 m. How much work does it take to bring them together?

Homework Equations

$$\Delta$$PE = ( k Q1 Q2 ) / r

Work = - $$\Delta$$PE

k= 8.99 e 9

The Attempt at a Solution

PE final = k Q1 Q2 / r
= (8.99e9)(3.3e-6)(7.6e-6) / ( 2.6m)
= 0.0868 J

PE initial = k Q1 Q2 / r
with r initial being infinitely large PE initial is basically 0

so $$\Delta$$PE = 0.0868 + 0
Work = - $$\Delta$$PE = -0.0868What is the error in this? Thank you!

 

[ehild]

Is the separation 2.6 m or 2.8 m? And do not forget the unit of work!ehild

 

[rbraunberger]

It was 2.6m...I fixed it. I found that the answer was just 0.0868 not -0.0868. My teacher said the equation was Work = -$$\Delta$$PE, but I found it some place else that shows it as just Work = $$\Delta$$PE. Which is correct?

 

[ehild]

The work needed to bring the charges together was the question. It is some external force Fe (maybe your force) that does this work. The external force is opposite and at least equal in magnitude with the Coulomb force Fe=-Fc. As the charges repel each other, the external force must push them toward the centre, so the direction of the external force is the same as the displacement: the work is positive.

ehild