Calculate W for Point Charge Configuration

[StephenDoty]

If you calculate W, the amount of work it took to assemble this charge configuration if the point charges were initially infinitely far apart, you will find that the contribution for each charge is proportional to {kq^2}/{L}. In the space provided, enter the numeric value that multiplies the above factor, in W. (See Picture Below)

delta U= -W
delta U= q*delta V

I tried using this idea but my answers are wrong. Like for charge A I got delta V= kq/sqrt(2)*L
or delta U= kq^2/sqrt(2)*L thus W = -kq^2/sqrt(2)*L

But the work for charge A equals 0. So what am I doing wrong?

Thanks
Stephen

 

[Doc Al]

I tried using this idea but my answers are wrong. Like for charge A I got delta V= kq/sqrt(2)*L
or delta U= kq^2/sqrt(2)*L thus W = -kq^2/sqrt(2)*L

This only considers the charge pairs that include A. (Why the negative sign?)

To find the total work done you must consider every pair of charges: A-B, A-C, A-D, B-C, and so on.

 

[StephenDoty]

W=-delta*U

So what formula do I need to use?

 

[StephenDoty]

the total potential energy=2kq^2/L

so would the work=-2kq^2/L?

 

[Doc Al]

the total potential energy=2kq^2/L

so would the work=-2kq^2/L?

How did you determine this value for PE?

As I'm sure you know, the potential energy between two charges separated by a distance r = $kq_1q_2/r$. Not that the PE is zero at infinity, thus the work done to move these two particles from infinity to a distance r is just $kq_1q_2/r$ (no need for a negative sign).

To find the total potential energy for all four particles, add up the potential energy contribution of each pair of charges. List each distinct pair (there are six) and its potential energy.

 

[highcoughdrop]

http://www.physics.umd.edu/courses/Phys260/agashe/S09/solutions/HW11.pdf