# Monopole Moment of a sphere of charge

In summary, the conversation discusses finding the monopole moment of a continuous charge distribution with a charge of \sigma = const*cos(\theta). The appropriate formula for this is p = \int r'\rho(r')d\tau, which simplifies to p = \int r' \sigma da for a surface charge. The individual attempts at solving the problem involve double integrals, but it is pointed out that the monopole moment is actually zero and some of the formulas used are incorrect.

## Homework Statement

I'm really bad at these type of problems. I'm supposed to find the monopole moment of this continuous charge distribution. its charge is

$$\sigma = const*cos(\theta)$$

## Homework Equations

$$p = \int r'\rho(r')d\tau$$
which then since we are doing a surface charge should be
$$p = \int r' \sigma da$$

## The Attempt at a Solution

Well, I want to do the double integral of something to find the charge distribution so I can find the monopole moment. I'm thinking something like
$$p = \int_{0}^{2 \pi}\int_{0}^{2 \pi} r' * c \cdot cos(\theta) sin( \theta) r^2 d\phi d\theta$$
and I'm thinking that r' is just r so then it would be

$$p = \int_0^{2\pi} d\phi \int_0^{\pi} r'^3cose(\theta)sin(\theta)d\theta$$

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The obvious problem that then comes up is that then appears is that I get a 0 term from the second integral that makes my whole monopole moment zero. Is this correct?

if you are supposed to calculate the monopole moment then you integrate the charge density only. the formulas you have above are those for a dipole moment. monopole moment is just total charge

The monopole moment is zero. Some of your formulas are wrong, as Capt. pointed out.

Ok, thanks! I think I see what I did wrong!

## 1. What is the Monopole Moment of a sphere of charge?

The Monopole Moment of a sphere of charge is a measure of the distribution of electric charge within a spherical object. It is a scalar quantity that describes the strength of the electric field generated by the object.

## 2. How is the Monopole Moment of a sphere of charge calculated?

The Monopole Moment of a sphere of charge is calculated by multiplying the total charge of the sphere by the radius of the sphere. This is represented by the formula: Qr, where Q is the charge and r is the radius.

## 3. What is the significance of the Monopole Moment of a sphere of charge?

The Monopole Moment of a sphere of charge is significant because it tells us about the strength and distribution of electric charge within a spherical object. It is also useful in understanding the behavior of electric fields and their interactions with other charged objects.

## 4. How does the Monopole Moment of a sphere of charge differ from the Dipole Moment?

The Monopole Moment of a sphere of charge is a measure of the overall charge distribution within a spherical object, while the Dipole Moment is a measure of the separation between two opposite charges. While the Monopole Moment is a scalar quantity, the Dipole Moment is a vector quantity.

## 5. Can the Monopole Moment of a sphere of charge be negative?

No, the Monopole Moment of a sphere of charge cannot be negative. It is a scalar quantity and represents the magnitude of the charge distribution, which is always positive. However, the direction of the electric field produced by the sphere can be positive or negative depending on the direction of the charge distribution.

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