What is the potential at point P at the center of this arc?

1. Feb 2, 2014

bbuilder

1. The problem statement, all variables and given/known data

What is the potential at point P due to a point charge Q at a distance R from P? Set V=0 at infinity. The same charge has been spread uniformly over a circular arc of radius R and central angle of 40 degrees. What is the potential at point P at the center of this arc?

2. Relevant equations
F=qE
E=kq/r^2
W=Fd
V=W/q

3. The attempt at a solution
After using the equations, I got V=(kQ)/R. I think the arc would be found in a similar way, but I don't know how to take the shape into account.

2. Feb 2, 2014

rude man

Integrate k dq/R over the 40 deg. k and R are constants. Express dq in terms of line charge density and d(theta).

3. Feb 2, 2014

haruspex

What would be the potential from 2 charges each Q/2 and each at distance R from P? What about 3 of Q/3 each? ...

4. Feb 2, 2014

bbuilder

Would the potential for the arc be the same as the potential of the point because potential is scalar?

5. Feb 2, 2014

haruspex

Merely being scalar doesn't do it. Scalars can be positive or negative.
But there are two facts you can use:
- the potential due to a charge depends only on the magnitude of the charge and how far away it is

6. Feb 3, 2014

rude man

It also depends on the polarity of the charge.

7. Feb 3, 2014

haruspex

Ok, value of the charge.