Calculating Dipole Moment for Spherical Surface of Radius R

As for 'good' questions, it really depends on your level of understanding and what you feel would help solidify your understanding of the material. You could start with the easier problems and work your way up to the more challenging ones, or focus on specific types of problems that you struggle with. Ultimately, it's important to practice enough problems to feel comfortable with the concepts before moving on to the next chapter.
  • #1
stunner5000pt
1,461
2
Griffith' E&M problem 3.28 page 151

Given a spherical surface of radius R which carries a surface charge [itex] \simga = k \cos\theta [/itex]

Calculate the dipole moment of this charge distribtuion

well using this equation

[tex] \vec{p} = \int \vec{r'} \sigma(\theta') dA' = \int Rk \cos\theta R^2 \sin\theta d\theta d\phi [/tex]

but i was told that this setup is wrong that - tat the first term in the integration which i have as R should be [itex] R \cos\theta[/itex] why is that??

what about my area element is that correct?

Please help

thank you in advance!
 
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  • #2
A simple dipole moment of two charges is the magnitude of the charge times the distance between them pointing from negative to positive. Taken from their center of charge that would be the sum of the products of the charges times the position vector from the center. You are adding a bunch of charges that are positive in the upper half space and negative in the lower half with cylindrical symmetry. You need the z coordinates of each bit of charge times the charge. The z coordinate is R*cosθ. The area element is OK.
 
Last edited:
  • #3
OlderDan said:
A simple dipole moment of two charges is the magnitude of the charge times the distance between them pointing from negative to positive. Taken from their center of charge that would be the sum of the products of the charges times the position vector from the center. You are adding a bunch of charges that are positive in the upper half plane and negative in the lower half with cylindrical symmetry. You need the z coordinates of each bit of charge times the charge. The z coordinate is R*cosθ. The area element is OK.

that makes sense now thanks!

do you have griffith's textbook
what do you think are 'good' questions to do in the 'more problem' section for chapter 3?
15 questions seems rather arduous since i would liek to go onto chapter 4...
 
  • #4
stunner5000pt said:
that makes sense now thanks!

do you have griffith's textbook
what do you think are 'good' questions to do in the 'more problem' section for chapter 3?
15 questions seems rather arduous since i would liek to go onto chapter 4...
No I don't have the book
 

1. What is a dipole moment and how is it calculated for a spherical surface of radius R?

A dipole moment is a measure of the separation of opposite electric charges within a molecule or system. It is calculated as the product of the charge and the distance between the charges. For a spherical surface of radius R, the dipole moment can be calculated by multiplying the magnitude of the charge by the distance from the center of the sphere to the point where the charge is located.

2. How do you determine the direction of the dipole moment for a spherical surface?

The direction of the dipole moment for a spherical surface can be determined by considering the direction of the electric field at the surface. The dipole moment will point in the direction of the electric field lines, from the positive to the negative charge.

3. Can a dipole moment exist on a perfectly symmetrical spherical surface?

No, a dipole moment cannot exist on a perfectly symmetrical spherical surface because the charges would be evenly distributed and there would be no separation of opposite charges.

4. How is the dipole moment affected by the size of the spherical surface?

The dipole moment is directly proportional to the size of the spherical surface. As the radius of the sphere increases, the distance between the charges also increases, resulting in a larger dipole moment.

5. Can the dipole moment of a spherical surface be altered by changing the charge or radius?

Yes, the dipole moment can be altered by changing the charge or radius of the spherical surface. An increase in charge or radius will result in a larger dipole moment, while a decrease in charge or radius will result in a smaller dipole moment.

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