Solution Found!
A solid sphere, radius R, is centered at the origin. The
Chapter 3, Problem 35P(choose chapter or problem)
A solid sphere, radius R, is centered at the origin. The “northern” hemisphere carries a uniform charge density \(\rho_{0}\), and the “southern” hemisphere a uniform charge density −\(\rho_{0}\). Find the approximate field E(r,θ) for points far from the sphere (r ≫ R).
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Questions & Answers
QUESTION:
A solid sphere, radius R, is centered at the origin. The “northern” hemisphere carries a uniform charge density \(\rho_{0}\), and the “southern” hemisphere a uniform charge density −\(\rho_{0}\). Find the approximate field E(r,θ) for points far from the sphere (r ≫ R).
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ANSWER:
Step 1 of 3
As the total charge for the full sphere is zero, we have to use the concept of a dipole. The diagram of the following problem can be shown as below:
The electric field for a dipole at any distance is given by,
The dipole moment is,
