Introduction to Electrodynamics · Problem 3.49

Potentials — David J. Griffiths

Physics · dipole-field-delta-function

Problem

In Ex. 3.9, we obtained the potential of a spherical shell with surface charge σ(θ)=kcos⁡θ\sigma(\theta) = k\cos\theta. In Prob. 3.30, you found that the field is pure dipole outside; it's uniform inside (Eq. 3.86). Show that the limit R→0R \to 0 reproduces the delta function term in Eq. 3.106.

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