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

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Homework Help Overview

The discussion revolves around calculating the electric potential at point P, located at the center of a circular arc, due to a point charge Q and a uniformly distributed charge along the arc. The problem involves understanding the implications of charge distribution and the nature of electric potential.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the calculation of potential using integration and charge density. There are inquiries about the effects of distributing the charge over the arc versus using a point charge. Some participants question whether the potential from the arc can be treated the same as that from a point charge, considering the scalar nature of potential.

Discussion Status

Participants are actively engaging with the problem, suggesting integration techniques and exploring different configurations of charge distribution. There is a recognition of the additive nature of potentials and the importance of charge magnitude and distance, though no consensus has been reached on the specific calculation method.

Contextual Notes

Participants are navigating the implications of charge distribution and the assumptions regarding potential at point P, including the relevance of the arc's geometry and the scalar nature of electric potential.

bbuilder
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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.
 
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Integrate k dq/R over the 40 deg. k and R are constants. Express dq in terms of line charge density and d(theta).
 
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? ...
 
Would the potential for the arc be the same as the potential of the point because potential is scalar?
 
bbuilder said:
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
 
haruspex said:
- 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.
 
rude man said:
It also depends on the polarity of the charge.
Ok, value of the charge.
 

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