Monopole,dipole,quadropole moment

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In summary, we are looking at a scenario where a point charge +Q is placed at the origin and a charge -Q is smeared around the origin with cylindrical symmetry around the Z axis. We want to show that when the charge distribution is prolate (egg-shaped), the monopole and dipole moments are zero but the quadrupole moment Q is positive. Similarly, when the charge distribution is oblate (pizza-shaped), the monopole and dipole moments are zero but the quadrupole moment is negative. To solve this problem, we can use the quadropole relation to determine the sign of Q, but we need to understand how the monopole and dipole terms become zero. This can be done by using
  • #1
klp_l123
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a point charge +Q is placed at the origin and a charge -Q is smeared around the origin maintaining cylindrical symmetry around the Z axis.Show that (i) when the charge distribution is prolate(egg-shaped),the monopole and dipole moments are zero but the quadrupole moment Q is positive; (ii) when the charge distribution is oblate(pizza-shaped),the monopole and dipole moments are again zero but the quadrupole moment is negative. please help me solving this problem ...
 
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  • #2
Well what have you tried so far?
 
  • #3
by the quadropole relation what we know, i can say about the +ve and -ve sign of Q ... but i cannot understand about monopole & dipole term- how they are goinh to zero ...
 
  • #4
Start with the formulas for the monopole "moment" (i.e. charge) and dipole moment. Do you know those?
 

1. What is a monopole moment?

A monopole moment refers to the electric charge distribution of a system, which can be represented by a single point charge. It is a measure of the strength of the electric field produced by the charge distribution.

2. How is a dipole moment different from a monopole moment?

A dipole moment refers to the separation of equal and opposite charges in a system, resulting in a positive and negative pole. This is different from a monopole moment, which represents a single point charge.

3. What is a quadropole moment?

A quadropole moment is a measure of the distribution of two equal but opposite dipole moments in a system. It represents the asymmetry of the charge distribution in a system.

4. How are these moments used in physics?

These moments are used to describe and analyze the electric properties of systems. They are particularly useful in studying the behavior of atoms, molecules, and other small particles in an electric field.

5. Can monopole, dipole, and quadropole moments exist in isolation?

No, these moments are always associated with a charge distribution. A monopole moment cannot exist without a charge, and a dipole moment cannot exist without two opposite charges. Similarly, a quadropole moment cannot exist without two dipole moments.

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