How Is Work Calculated When Moving a Charge in an Electric Field?

[smartdesk]

Homework Statement

What is the work done in moving a 0.2 µC point charge from corner a to b of a square abcd, when a 10 µC charge exists at the center of the square?

Homework Equations

Work or ΔU=q*V
V=kq/r

The Attempt at a Solution

V=kq/r
V=(9.0x10^9)(0.2x10^-6)/r

This is where I get stuck because there is no r given. We can assume that all the sides of the square are equal and the distance to the 10 µC charge is half of that. But I feel like an actual value should be given.

 

[Borek]

Assume some length of the square side, see if it doesn't cancel out in the final result.

 

[smartdesk]

I assumed the length of he side of the square to be 0.3m, but it doesn't cancel out. So if the side were 3m, electric potential and work done would be:
V=kq/r=(9.0*10^9)(0.2*10^-6)/3=600 N

ΔU=q*V=(0.2*10^-6)(600)=1.2*10^-4 J

 

[smartdesk]

i meant 3m not 0.3 m

 

[ap123]

Hi smartdesk

Work out the potential energy of the system when the charge is at a and then again when the charge is at b, and then compare them.
Just use r for the distance.

Notice anything?

 

[Borek]

Work or ΔU=q*V

That's not correct. Electric force is conservative, which means work done depends on the difference between potential in the starting and ending point. So the more correct way of expressing it would be ΔU=q*ΔV. Now think what ΔV is.

Edit: ap123 answered while I was composing the answer, but we are aiming at exactly the same thing.