Simple Point Charge Potential Problem

In summary, the problem involves two point charges on the x-axis with opposite sign and equal magnitude. The goal is to find the potential at a point z above the center of the charge distribution. The equation to be used is V(r) = \frac{1}{4\pi\epsilon\stackrel{}{0}}\sum\frac{q\stackrel{}{i}}{r\stackrel{}{i}} and the point of analysis is at (0,z). The confusion in the attempt at solution is due to the assumption that the distance to the point is just \sqrt{z\stackrel{2}{}+(\frac{d}{2})\stackrel{2}{}} without considering the direction of the
  • #1
dgreenheck
23
0

Homework Statement


There are two point charges aligned on the X-axis. Charge A is a distance -d/2 from the origin and Charge B is a distance d/2 from the origin. What is the potential at a distance z above the center of the charge distribution?

To further clarify
Charge A location at (-d/2,0)
Charge B location at (d/2,0)
Point of analysis at (0,z)

Homework Equations


V(r) = [itex]\frac{1}{4\pi\epsilon\stackrel{}{0}}[/itex][itex]\sum\frac{q\stackrel{}{i}}{r\stackrel{}{i}}[/itex]

The Attempt at a Solution


I'm confused because I'm getting 0 and the answer should be non-zero. There is no direction information carried in r, correct? Because it's just supposed to be the distance to point (0,z) which is [itex]\sqrt{z\stackrel{2}{}+(\frac{d}{2})\stackrel{2}{}}[/itex]. And since the charges are of opposite sign, the sum will cause them to cancel out. Obviously my understanding of the summation is wrong here so if someone could point me in the right direction that would be very helpful. Thanks
 
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  • #2
dgreenheck said:
1. Homework Statement
There are two point charges aligned on the X-axis. Charge A is a distance -d/2 from the origin and Charge B is a distance d/2 from the origin. What is the potential at a distance z above the center of the charge distribution?

To further clarify
Charge A location at (-d/2,0)
Charge B location at (d/2,0)
Point of analysis at (0,z)

Homework Equations


V(r) = [itex]\frac{1}{4\pi\epsilon\stackrel{}{0}}[/itex][itex]\sum\frac{q\stackrel{}{i}}{r\stackrel{}{i}}[/itex]

The Attempt at a Solution


I'm confused because I'm getting 0 and the answer should be non-zero. There is no direction information carried in r, correct? Because it's just supposed to be the distance to point (0,z) which is [itex]\sqrt{z\stackrel{2}{}+(\frac{d}{2})\stackrel{2}{}}[/itex]. And since the charges are of opposite sign, the sum will cause them to cancel out. Obviously my understanding of the summation is wrong here so if someone could point me in the right direction that would be very helpful. Thanks

I "bolded" a couple of parts of your original post.

Are these charges equal in magnitude? Are these charges of the same sign or opposite sign?
 
  • #3
The charges are of opposite sign and of equal magnitude.
 

1. What is a simple point charge potential problem?

A simple point charge potential problem is a type of electrostatics problem in which a single point charge is placed in an electric field and its potential energy is calculated at various points in space.

2. What is the formula for calculating the potential energy in a simple point charge potential problem?

The formula for calculating potential energy in a simple point charge potential problem is V = kQ/r, where V is the potential energy, k is the Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge to the point at which the potential energy is being calculated.

3. How is a simple point charge potential problem different from other electrostatics problems?

A simple point charge potential problem is different from other electrostatics problems because it involves only one point charge, whereas other problems may involve multiple charges and more complex geometries.

4. What are some real-world applications of simple point charge potential problems?

Simple point charge potential problems have many real-world applications, such as calculating the potential energy of an electron in an atom, determining the potential energy of a charged particle in a particle accelerator, and analyzing the electric potential of a single neuron in the brain.

5. How can I solve a simple point charge potential problem?

To solve a simple point charge potential problem, you can use the formula V = kQ/r and plug in the values for k, Q, and r that are given in the problem. You can also use the concept of equipotential lines, which are lines that connect points with equal potential energy, to visualize the electric field and potential energy distribution around the point charge.

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