Electric Potential: Find Distance/Ratio of Charges

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In summary, the problem involves a positive charge +q1 located to the left of a negative charge -q2, with two points on a line between them where the total potential is zero: one 3.35 cm to the left of -q2 and the other 7.65 cm to the right of -q2. To solve for the distance between the charges, we can use the equation V=kq/r, where V is the potential, k is a constant, q is the charge, and r is the distance. By setting the potential equations at the given points equal to each other and solving for r, we can determine the distance between the charges. Additionally, we can find the ratio of the magnitudes of the
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pmd28
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Homework Statement


A positive charge +q1 is located to the left of a negative charge −q2. On a line passing through the two charges, there are two places where the total potential is zero. The first place is between the charges and is 3.35 cm to the left of the negative charge. The second place is 7.65 cm to the right of the negative charge.
(a) What is the distance between the charges?
(b) Find |q1|/|q2|, the ratio of the magnitudes of the charges

Homework Equations


V=kq/r


The Attempt at a Solution


I don't know where to start. I know that I need to solve for the distance between +q1 and the spot 3.35 cm to the left of the negative charge to be able to solve for the distance between them. I'm just not sure how to use the charge to the right of -q2.
 
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  • #2
Start by drawing a diagram of the setup. Label the distance between the charges as d.

What equations can you write to describe the given conditions?
 
  • #3
See that's the thing, I'm still iffy on the relationshiphs. My best educated guess would be:

Since V @ .0335m is equal to zero. That would mean the net electric field at that point is also 0 because E=-ΔV/Δs.

Or am I going in a completely wrong direction.
 
  • #4
pmd28 said:
See that's the thing, I'm still iffy on the relationshiphs. My best educated guess would be:

Since V @ .0335m is equal to zero. That would mean the net electric field at that point is also 0 because E=-ΔV/Δs.

Or am I going in a completely wrong direction.

You can work with the electric field or the potential. The potential is simpler as it is a scalar value that depends only on the charge and the distance from it. Since the problem statement specifically mentions potential, that would suggest that potential is a likely way to proceed :smile:

What's the expression for the electric potential at a distance r from a charge q?
 
  • #5
V=kq/r
 
  • #6
pmd28 said:
V=kq/r

Yes, that's correct. So write expressions for the potential at the two given locations assuming that the distance between the charges is d.
 
  • #7
Ok, sorry I had a spark of genius. And I've been kind of going with it. I just want to know if I'm on the right track. I set the +q1 charges equal to each other and got:

r=.11/(V1-V2)

Then I set the -q2 charges equal to each other and got:

.035V1=.0765V2

Substitute to get

r=.11/(V1-.035V1)

I got stuck again. I need one more equation, but I just can't seem to find it.
 
  • #8
pmd28 said:
Ok, sorry I had a spark of genius. And I've been kind of going with it. I just want to know if I'm on the right track. I set the +q1 charges equal to each other and got:

r=.11/(V1-V2)

Then I set the -q2 charges equal to each other and got:

.035V1=.0765V2

Substitute to get

r=.11/(V1-.035V1)

I got stuck again. I need one more equation, but I just can't seem to find it.
You'll have to explain the above in detail. I don't understand what the equations are meant to represent. In particular, what are the "+q1 charges" and "-q2 charges"? The problem statement mentions only two charges, +q1 and -q2. And the potentials of interest are both zero.
 
Last edited:
  • #9
The problem states a "-q2" not a "+q2".
 
  • #10
Nvm I solved it. Thanks :D
 

1. What is electric potential?

Electric potential is the amount of electric potential energy per unit charge at a given point in an electrical field. It is a measure of the amount of work required to move a unit charge from one point to another within the field.

2. How do you find the distance between two charges?

To find the distance between two charges, you can use the equation d = √(kq1q2/V), where d is the distance, k is the Coulomb constant, q1 and q2 are the magnitudes of the two charges, and V is the electric potential. This equation can be derived from Coulomb's Law and the definition of electric potential.

3. How do you find the ratio of charges using electric potential?

The ratio of charges can be found by using the equation q1/q2 = V1/V2, where q1 and q2 are the magnitudes of the two charges and V1 and V2 are the electric potentials at two different points. This equation can also be derived from Coulomb's Law and the definition of electric potential.

4. What are the units of electric potential?

The units of electric potential are volts (V), which is equivalent to joules per coulomb (J/C) in SI units. Electric potential is also sometimes expressed in terms of electron volts (eV), where 1 eV is equal to the amount of energy gained by an electron when it is accelerated through a potential difference of 1 volt.

5. How is electric potential related to electric field?

Electric potential is related to electric field by the equation E = -∇V, where E is the electric field, V is the electric potential, and ∇ is the gradient operator. This means that the electric field is the negative gradient of the electric potential, and it points in the direction of decreasing potential. In other words, the electric field is a measure of the change in electric potential over a given distance.

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