What is the relationship between electric potential and work done?

[ojsimon]

Hi

I am sure this is very basic but i am struggling to derive or work this out, and i have looked, on the internet and textbooks and can't find this.

The electric potential at a point is defined as the work done per unit charge to move a small test charge from infinity to that point.

And an equation for it is : EP = k*(Q/R)

I want to get back to the definition from this equation, but i can't get very far:

here is what i have done: WD= work done

Q/R = (wd/v)/R
= wd/vR


But i can't go much further without it just going back to the original form... Can anyone help me?

Thanks

 

[tiny-tim]

hi ojsimon!

(what's v ? )

work done = ∫ force d(distance) = ∫_∞^R kQ/r² dr

(and d(work done)/dr = force)

 

[ojsimon]

sorry v was meant to be voltage and came from the equation v=wd/q

Thanks although i don't quite understand your integral?

Thanks

 

[tiny-tim]

Thanks although i don't quite understand your integral?

The integral is the force integrated from infinity to the distance R, since the PE is the work done to get the charge from infinity to R.