Why electric potential of arc treated like point charge

In summary, the solution to finding V of Arc of uniform charge at the center (or origin) is to use kQ/R. This works for any shape because the electric potential is a scalar.
  • #1
lonewolf219
186
2

Homework Statement



Give an expression to find V of Arc of uniform charge (at the center, or origin)

Homework Equations



V=kQ/R


The Attempt at a Solution



the solution is kQ/R. I'm wondering why an arc can be treated like a point charge...
Is this reason partly connected to a conducting sphere, and the fact is has an equal charge distribution everywhere, even at its hollow center? Likewise, would a uniform arc also be seen as a hollow conducting sphere?
 
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  • #2
hi lonewolf219! :smile:

electric potential is a scalar, and so we add the contributions (from different parts) as scalars (ie ordinary numbers) …

this works for any shape :wink:

(unlike electric field, which is a vector, and so we add the contributions as vectors)
 
  • #3
Thanks Tiny-Tim...

Just starting the second semester of introductory physics. A little confusing with electric force, electric field, electric potential and electric potential energy...

As you pointed out, scalars versus vectors. But I guess there is little connection between an arc and a conducting sphere...
 
  • #4
lonewolf219 said:

Homework Statement



Give an expression to find V of Arc of uniform charge (at the center, or origin)

the solution is kQ/R. I'm wondering why an arc can be treated like a point charge...

You can consider the arc as a lot of equal point charges arranged in arc from. A line element dL has a charge dQ, and contributes to the potential by dV= kdQ/R at the centre. The contributions of the charges add up: so the total potential at the centre is the integral of these contributions.

[itex]V=\int{\frac{kdQ}{R}}[/itex].

k/R is constant, it can be factored out from the integral, so [itex]V=\frac{k}{R}\int{dQ}=\frac{kQ}{R}[/itex].

ehild
 

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  • #5
hi lonewolf219! :smile:

(just got up :zzz: …)
lonewolf219 said:
A little confusing with electric force, electric field, electric potential and electric potential energy...

electric force is a force (as in "F = ma")

electric field is electric force per charge

electric potential energy is what it says, the PE of the electric field

electric potential is electric potential energy per charge

(just as gravitational potential is gravitational potential energy per mass: PE/m = mgh/m = gh, or = -mMG/mr = -MG/r)
 
  • #6
Thanks guys!

People like you are the reason physics forums is so awesome...
 

1. Why is electric potential of arc treated like a point charge?

The electric potential of an arc is treated like a point charge because it is a concentrated source of electric charge. This allows for simplified calculations and analysis of the electric field and potential around the arc.

2. Can't the electric potential of an arc be treated as a distributed charge instead of a point charge?

While the electric potential of an arc can technically be treated as a distributed charge, it is typically approximated as a point charge due to the small size and concentrated nature of the arc. This simplification allows for easier calculations and better understanding of the behavior of the arc.

3. How does treating the electric potential of an arc as a point charge affect its behavior?

Treating the electric potential of an arc as a point charge does not significantly affect its behavior, as the small size and concentrated nature of the arc make this approximation valid. However, it does allow for easier analysis and calculation of the electric field and potential around the arc.

4. What are the limitations of treating the electric potential of an arc as a point charge?

The main limitation of treating the electric potential of an arc as a point charge is that it is only a simplification and may not accurately represent the true behavior of the arc. This approximation is valid for small arcs, but may not hold true for larger arcs or arcs with varying shapes or sizes.

5. Are there any alternative methods for calculating the electric potential of an arc?

Yes, there are alternative methods for calculating the electric potential of an arc, such as using more advanced mathematical models or experimental techniques. However, treating the arc as a point charge is a commonly used and valid approach for simpler calculations and analysis.

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