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

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SUMMARY

The potential at point P, located at the center of a circular arc with a central angle of 40 degrees, due to a uniformly distributed point charge Q at a distance R, is calculated using the formula V=(kQ)/R. The discussion emphasizes that the potential is scalar and additive, meaning that the total potential from multiple charges can be summed directly. It also highlights that the potential depends solely on the magnitude of the charge and its distance from the point of interest, regardless of the charge's polarity.

PREREQUISITES
  • Understanding of electric potential and point charges
  • Familiarity with the equations: V=W/q, E=kq/r^2
  • Knowledge of integration techniques for continuous charge distributions
  • Concept of line charge density and its application
NEXT STEPS
  • Study the concept of electric potential due to continuous charge distributions
  • Learn about line charge density and its implications in electrostatics
  • Explore the principle of superposition in electric potential
  • Investigate the effects of charge polarity on electric potential
USEFUL FOR

Students and educators in physics, particularly those focusing on electrostatics and electric potential calculations, as well as anyone preparing for exams in electromagnetism.

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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