# Work--please check my work for me

• Feb 1st 2011, 09:43 AM
zhupolongjoe
Work--please check my work for me
Electrons repel each other with a force that is inversely proportional to the square of the distance between them, call the proportionality constant k. Suppose one electron is fixed at x=0. Find the work done to move a second electron along the x-axis from the point x=10 to x=1.

So the F=k/x^2 and W=F*d, but what do I use for the distance? 10?

Would it just be integral (from 10 to 1) of 10k/x^2 dx?

Someone told me it would be integral (10 to 1) of k/x^2 dx without the 10, but what about the distance? This is what is confusing me.
• Feb 1st 2011, 09:47 AM
TheEmptySet
Quote:

Originally Posted by zhupolongjoe
Electrons repel each other with a force that is inversely proportional to the square of the distance between them, call the proportionality constant k. Suppose one electron is fixed at x=0. Find the work done to move a second electron along the x-axis from the point x=10 to x=1.

So the F=k/x^2 and W=F*d, but what do I use for the distance? 10?

Would it just be integral (from 10 to 1) of 10k/x^2 dx?

Someone told me it would be integral (10 to 1) of k/x^2 dx without the 10, but what about the distance? This is what is confusing me.

The distance is in your limits of integration. Remember that Work = Force $\times$ distance. If you think about it in terms of Reimann sums then You are multiplying the Nonconstant force by a tiny bit of distance dx and then adding up all of the contibutions to get the total amount of work done.
• Feb 1st 2011, 09:51 AM
zhupolongjoe
Ok, so just integral(10 to 1) k/x^2 would do it?
• Feb 1st 2011, 10:02 AM
TheEmptySet
Yep