Potential Due to collection of point charges

In summary, the electric potential at the point x=0 can be found by using the equation V=1/(4piEpsilon)Sigma(q/r), where q is the charge and r is the distance from the point. The total potential is the sum of all the separate potentials, which can be calculated using the equation V(0) = (Q/(4piEpsilon))*sum(1/2^i*a), where Q is the total charge and a is the distance between the point charges. The OP should try to evaluate this sum to find the electric potential at x=0.
  • #1
GingerBread27
108
0
As shown below, an infinite number of point positive charges of 8.0 C are placed on the x-axis at x=a, 2a, 4a, 8a, ... with a=18 cm. Find the electric potential (in V) at the point x=0.

0---a----2a---4a-----8a-------

Ok so I'm using the equation V=1/(4piEpsilon)Sigma(q/r). and it's not working! I don't understand what I'm doing wrong it should be pretty easy. Please help. I'm using 8 Coulombs as my q and r is my changing variable. I'm getting 88.88 and it's not working.
 
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  • #2
your method is fine... what is your answer in term of V,q,a...etc? (not the numerical value )
the following equation might help you
[tex] \sum_{x=0}^\infty \frac{1}{2^x} = 2 [/tex]
 
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  • #3
Your total potential is just the sum of all the separate potentials, so:
[tex]V(0) = \frac{Q}{4\pi\epsilon_0} \sum_{i=0}^\infty \frac{1}{2^i a}
[/tex]

Now try to evaluate this sum and you'll get your answer :rolleyes:
 
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  • #4
-blah- stupid
 
  • #5
sory, typo
please don't give out the answer...
leave some work for the OP to do
 

1. What is the formula for calculating the potential due to a collection of point charges?

The formula for calculating the potential due to a collection of point charges is V = k * q / r, where V is the potential, k is the Coulomb's constant, q is the charge of the point charges, and r is the distance between the point charge and the point where the potential is being calculated.

2. How does the distance between point charges affect the potential due to their collection?

The potential due to a collection of point charges is inversely proportional to the distance between the point charges. This means that as the distance increases, the potential decreases.

3. Can the potential due to a collection of point charges be negative?

Yes, the potential due to a collection of point charges can be negative. This occurs when the point charges have opposite signs and the resulting potential is attractive rather than repulsive.

4. Does the number of point charges in a collection affect the overall potential?

Yes, the number of point charges in a collection does affect the overall potential. The more point charges there are, the higher the potential will be, assuming all other factors such as distance between charges and charge values are constant.

5. How is the potential due to a collection of point charges different from the potential due to a single point charge?

The potential due to a collection of point charges is the sum of the potentials due to each individual point charge. This is in contrast to the potential due to a single point charge, which only takes into account the potential at a specific point due to that single charge.

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