Work to move charges from Infinity to origin

[lachy89]

Homework Statement

Eight 3.0 μC charges are located at the corners of a unit cube centered about the origin with 1mm edges. How much work does it take to bring a 5.0 μC charge from infinity to the origin?

Homework Equations

U= k*q1*q2/r

The Attempt at a Solution

r= ((1*10^-3)^2+(1*10^-3)^2+(1*10^-3)^2))^(1/2)m
=1.73*10^-3m

U=(9*10^9)*(3*10^-6)*(5*10^-6)*8 / (1.73*10^-3)
=623.54 J

U at Infinite = 0

Work = 623.54 J
I have tried to explain why I have simply multiplied one result by 8 below.

The charge will have to have some path to get to the center of the cube and as a result there will be some time where it will be closer to some charges(a) than 1.73*10^-3m which would require more work to move the charge(b) closer than this. This extra work will be counter-acted as there will be negative work equal to this for the charge(b) to move away from the charge(a) once again.

Ok so this is the answer that I have obtained, unfortunately this is not one of the multiple choice options available. So I am not confident that I have completed the problem correctly, any feedback would be most welcomed.

 

[ehild]

The cube is centered about the origin. How far is the centre of a cube from the corners?

ehild

 

[lachy89]

Eight 3.0 μC charges are located at the corners of a "unit cube centered about the origin with 1mm edges"

r= ((1*10^-3)^2+(1*10^-3)^2+(1*10^-3)^2))^(1/2)m
=1.73*10^-3m

Wouldn't that be the distance?

 

[ehild]

No. Make a picture. What does it mean "centered about the origin? "

ehild

 

[lachy89]

Ok I think I have seen where I have made the mistake, thank you for your 'guidance' :)