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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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,