# Monopole & Dipole Homework: Sphere + Line Charge

• Varnson
In summary, the conversation discusses calculating the monopole and dipole moments of a uniformly charged line and sphere in relation to each other. The dipole moment is defined as the integral of the vector pointing from the source to the dipole moment. Superposition and the formula for changing the origin are suggested as a method for calculating the dipole moment. The conversation also mentions the influence of the sphere's charge on the total charge of the line and the forces between the two objects.
Varnson

## Homework Statement

A sphere of radius R and uniform charge density 'row' is situated at the origin. A uniformly charged line with length L and charge density 'lamda' (for simplicity assume L>2R) is a distance D from the origin in the y=0 plane and orientated so as to be parallel to the x-axis with is center on the z axis. What is the monpole moment of the line charge distribution? What is the dipole moment of the line charge distribution?

## The Attempt at a Solution

I need a little help visuallysing and getting started. Thanks for the help in advance!

The monopole moment should be easy, it's just the total charge. What is the definition of the dipole moment?

The dipole moment is the } r(s) * row * dtau Where } is the integral and r(s) is the vector pointing from source to the dipole moment. Would the charge of the sphere have any influence on the totla charge of the line?

No, the charges are as given. I'm sure you can assume all the appropriate forces are holding them in place, otherwise this would be a complicated dynamical problem.

That is what I was thinking. What vector would you choose for your source vector?

It's probably easiest to use superposition and the formula for changing the origin. Specifically, say you want to calculate the dipole moment with the origin at the center of the sphere. The part that comes from the sphere should be easy. If you get the part from the line, you can just add this to get the total moment. But rather than calculating this directly, you can calculate the moment of the line about the center of the line, and then shift from this origin to the original one at the center of the sphere.

Am I correct if I choose two arbitrary points at each end of the line to figure out the dipole for the line?

Also, if the line is moved a distance 'D' which is greater than 'R' would the force on it be zero? I am thinking no, because the force from the more top of the sphere is greater than the force on the bottom so they won't cancel out. I am assuming the same for the other two direction as well.

I don't know what you mean. If you choose two arbitrary points for what? And as far as the forces, as I said, you don't have to worry about them for this problem, but if you're just curious, there will always be a net force between the line and the sphere, unless they have charges of opposite signs and their centers coincide. There will also be sturcurual forces required to maintain their shapes, but these are more complicated.

## 1. What is a monopole and dipole?

A monopole is a type of charge distribution where there is only one type of charge (either positive or negative) present. A dipole, on the other hand, is a charge distribution where there are both positive and negative charges present, but they are separated by a distance.

## 2. How do monopoles and dipoles affect electric fields?

Monopoles do not have a significant effect on electric fields, as there is no separation of charges. Dipoles, however, create electric fields that vary in strength and direction depending on the orientation of the dipole.

## 3. What is the difference between a sphere and a line charge?

A sphere charge is a type of charge distribution where the charge is uniformly distributed on the surface of a sphere. A line charge, on the other hand, is a charge distribution that is concentrated along a line, with no charge present outside of the line.

## 4. How do you calculate the electric potential for a sphere and line charge?

The electric potential for a sphere charge can be calculated using the equation V = kQ/r, where k is the Coulomb's constant, Q is the charge on the sphere, and r is the distance from the center of the sphere. For a line charge, the electric potential can be calculated using the equation V = kλ ln(r2/r1), where λ is the charge density along the line and r1 and r2 are distances from the line charge.

## 5. How does the distance from a monopole or dipole affect the electric field?

The electric field from a monopole decreases as the distance from the charge increases, following an inverse square law. For a dipole, the electric field varies in strength and direction depending on the distance and orientation of the dipole.

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