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Griffith's EM problem 3.28

A spherical shell of radius R has a surface charge [itex] \sigma = k \cos \theta [/itex]

a) Calculate the dipole moment of this charge distribution.

i know that

[tex] p = r' \sigma(r') da' [/tex]

but here sigma depends on theta

would the dipole moment p then turn into

[tex] p = \theta' \sigma(theta') da' [/tex]

and the radius of the sphere is constant theta and phi are constant

so that

[tex] p = \int_{0}^{\pi} \int_{0}^{2 pi} \theta' \sigma(\theta') R^2 \sin\theta' d \theta' d \phi [/tex]

i get a negative dipole moemnt as a result of this though... which amkes no sense

what am i doing wrong??

please help!!!

thanks :)

A spherical shell of radius R has a surface charge [itex] \sigma = k \cos \theta [/itex]

a) Calculate the dipole moment of this charge distribution.

i know that

[tex] p = r' \sigma(r') da' [/tex]

but here sigma depends on theta

would the dipole moment p then turn into

[tex] p = \theta' \sigma(theta') da' [/tex]

and the radius of the sphere is constant theta and phi are constant

so that

[tex] p = \int_{0}^{\pi} \int_{0}^{2 pi} \theta' \sigma(\theta') R^2 \sin\theta' d \theta' d \phi [/tex]

i get a negative dipole moemnt as a result of this though... which amkes no sense

what am i doing wrong??

please help!!!

thanks :)

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