How Much Work Is Required to Exchange q2 and q3?

[quebecois22]

Homework Statement

How much work is required to exchange the positions of q2 and q3?

q2 q3


q1

q1 and q2 are separated by a distance of 4.00 cm and q2 and q3 are separated by a distance of 2.00cm

The charge on q1 is 5.00nC, q2 is -5.00nC and q3 is 10.0nC

Homework Equations

U=(K(q2)(q3))/(r23) (#1)
U=qV (#2)

The Attempt at a Solution

Since the energy required to hold these charges at their positions is equation 1, my guess to simply found the energy holding the charges and that would be the energy required to move them... Guess I'm wrong...

Any help is appreciated...

 

[CanIExplore]

Can you help us picture the charge configuration? I'm guessing they're all lying on the same line but can you clarify this for me. How are they oriented with respect to each other?

 

[nickjer]

Work is just the change in potential energy. So just find the difference in the final and initial total potential energies.

So write down the initial total potential energy and the final total potential energy.

 

[quebecois22]

@CanIExplore:

They're positioned just like in my first post: q2 directly over q1 and q3 directly across q2.

Thx for your input,

@nickjer: Aren't both potential energies equal? I mean at the end the only difference is that they switched places...

 

[Saraphim]

If the concept of moving the charges around in an existing field is confusing you, try moving them to infinity and then back into their new positions and consider the work you're doing.

 

[nickjer]

quebecois22 the distance between charges q1 and q2 will change, as well as q1 and q3. So the total potential energy will change.

 

[quebecois22]

I am completely lost...

I don't know how to take q1 into account... how does it behave on the two charges?

 

[nickjer]

The total potential energy of 3 particles is just U_{12} + U_{23} + U_{13}. You can probably find that in your book.

 

[quebecois22]

Ah so the final and initial potential energies will vary according to the distances between them...
So delta U is the energy required to shift q2 & q3 places?

 

[nickjer]

You want to find the different in total potential energy when you switch q2 and q3. It shouldn't be 0, unless q2=q3 or the distance between q1 and q2 is the same as between q1 and q3.

 

[quebecois22]

Yeah it's not so the difference won't yield zero...
So this difference in potential energies is the energy required to shift those two charges?

 

[nickjer]

Yes, since this is a conservative force.