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

[bbuilder]

Homework Statement

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?

Homework Equations

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

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.

 

[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).

 

[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? ...

 

[bbuilder]

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

 

[haruspex]

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

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

 

[rude man]

- the potential due to a charge depends only on the magnitude of the charge and how far away it is

It also depends on the polarity of the charge.

 

[haruspex]

It also depends on the polarity of the charge.

Ok, value of the charge.