# Calculating the electric potential

• physicsisfun0
In summary, the conversation discusses the problem of finding the electric potential inside and outside of a metal pipe that has been split into four sections with different electric potentials. The equations for electric potential and boundary conditions are provided, and the conversation concludes with a discussion on how to solve for the coefficients and use the boundary conditions to find the values of ao and bo.
physicsisfun0

## Homework Statement

We have the cross section of a metal pipe that has been split into four sections. Three of the sections have a constant electric potential, Vo. The fourth section is grounded so electric potential is zero. We are looking for electric potential inside and outside of the pipe.

## Homework Equations

For electric potential I have:
V = ao + boln(s) +Σ(sv(avcos(vφ) + bosin(vφ)) + s-v(cvcos(vφ) + dvsin(vφ))
We also know boundary conditions:

## The Attempt at a Solution

(I think this next part is right)
And electric potential inside becomes:
V = ao + boln(s) +Σ(sv(avcos(vφ) + bosin(vφ))
And electric potential outside becomes:
V = ao + boln(s) +Σs-v(cvcos(vφ) + dvsin(vφ))

There is also symmetry along the x-axis so we can ignore the sin(vφ) contribution:
V = ao + boln(s) +Σ(sv(avcos(vφ))
V = ao + boln(s) +Σ(s-v(avcos(vφ))

Do I need to solve for ao and bo? How would I use the boundary conditions?

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Welcome to PF!

physicsisfun0 said:
Note that the first equation above implies that ##7 \pi / 4## is less than ##\pi/4##. But, the intention is clear.

V = ao + boln(s) +Σ(sv(avcos(vφ))
V = ao + boln(s) +Σ(s-v(avcos(vφ))
OK, but it might be confusing to use the same notation for the coefficients for the two different regions.
Do I need to solve for ao and bo? How would I use the boundary conditions?
For the region inside the pipe, note that s can be zero. What does that tell you about the value of bo for the inside region?
For the region outside the pipe, note that s can become arbitrarily large. What does that tell you about bo for the outside region?

To find ao, set s equal to the radius of the pipe in the above two equations. For each equation, integrate both sides of the equation with respect to φ from 0 to 2π. The boundary condition tells you V as a function of φ for the integration of the left side.

To find other coefficients an, multiply both sides of the equation by cos(nφ) before integrating.

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Delta2

## What is electric potential?

Electric potential, also known as voltage, is a measure of the amount of potential energy per unit charge at a specific point in an electric field.

## How is electric potential calculated?

Electric potential can be calculated by dividing the work done in moving a charge from infinity to a specific point in an electric field by the amount of charge moved.

## What is the unit for electric potential?

The unit for electric potential is volts (V), which is equivalent to joules per coulomb (J/C).

## How does distance affect electric potential?

Distance plays a critical role in electric potential, as it follows an inverse-square law. This means that as distance increases, electric potential decreases at a rate of 1/r^2, where r is the distance between the point and the source of the electric field.

## What is the difference between electric potential and electric potential energy?

Electric potential is a measure of the amount of potential energy per unit charge at a specific point, while electric potential energy is the total amount of potential energy possessed by a charge in an electric field. In other words, electric potential is a per-unit measure, while electric potential energy is a total measure.

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