Electric Potential: Find Potential Everywhere from Two Point Charges

In summary, electric potential is a measure of the potential energy of an electric charge in an electric field. It can be calculated by dividing the potential energy of a charged object by its charge or by multiplying the electric field strength by the distance between two points. The electric field is the gradient of the electric potential and the two are closely related. The presence of two point charges affects the electric potential at a point through the principle of superposition. Some real-world applications of electric potential include electronics, particle accelerators, and energy storage devices.
  • #1
Crazy Gnome
13
0

Homework Statement


Two point charges q and -q are located on the z axis at (x,y,z) = (0,0,a) and (0,0,-a) respectively.

Find the potential [tex]\phi[/tex] everwhere



The Attempt at a Solution



I know all the equations and such, I just don't know how to integrate it. I am guessing that it is in cylindrical coordinates.
 
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  • #2
Why do you need to integrate it? Just find the potential at any point due to q and the one due to -q and add up the two. This one you can easily apply the formula for potential due to point charge.
 
  • #3


I would suggest approaching this problem by breaking it down into smaller, more manageable steps. First, let's start by defining the variables and constants involved. We have two point charges, q and -q, located at specific positions on the z-axis. We also have the coordinates (x,y,z) = (0,0,a) and (0,0,-a) for these charges. In addition, we have the potential, \phi, which we need to find everywhere.

Next, let's review the equations and concepts related to electric potential. The electric potential at a point in space is defined as the amount of work needed to bring a unit positive charge from infinity to that point. It is given by the equation \phi = kq/r, where k is the Coulomb constant, q is the charge, and r is the distance from the point charge. In this case, we have two point charges, so we will need to calculate the potential due to each charge separately and then add them together to find the total potential at a given point.

Now, let's consider the integration aspect of the problem. Since the charges are located on the z-axis, it would be most convenient to use cylindrical coordinates. This means we can express the distance, r, as \sqrt{x^2 + y^2}. We can then use this expression to calculate the potential due to each charge at any point in space.

To find the potential everywhere, we will need to consider all points in space, which means we will need to integrate over the entire space. This can be done by breaking it down into smaller steps, such as integrating over a small section of the z-axis at a time, and then summing up the contributions from each section. Alternatively, you can also integrate over the entire volume of space, using the volume element in cylindrical coordinates, which would be dV = r dr d\theta dz.

In summary, to find the potential everywhere, you will need to consider the equations and concepts related to electric potential, use cylindrical coordinates to calculate the potential due to each charge, and integrate over the entire space using appropriate methods. I hope this helps guide you in solving the problem.
 

1. What is electric potential?

Electric potential is a measure of the potential energy of an electric charge at a particular point in an electric field. It is measured in volts and represents the work that would be required to move a unit of electric charge from one point to another.

2. How is electric potential calculated?

Electric potential is calculated by dividing the potential energy of a charged object by the amount of charge it possesses. It can also be calculated by multiplying the electric field strength by the distance between the two points.

3. What is the relationship between electric potential and electric field?

The electric field is the gradient of the electric potential, meaning that the electric field points in the direction of decreasing potential. In other words, the electric field is the force per unit charge acting on a charged object, while the electric potential represents the potential energy per unit charge at a given point.

4. How do two point charges affect the electric potential at a point?

The electric potential at a point is affected by the presence of two point charges by the principle of superposition. This means that the total electric potential at a point is equal to the sum of the individual electric potentials created by each point charge.

5. What are some real-world applications of electric potential?

Electric potential has many practical applications, such as in determining the direction and strength of electric fields in electronics, designing and operating particle accelerators, and understanding the behavior of charged particles in space. It also plays a crucial role in the functioning of batteries and other energy storage devices.

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