Explain all reasoning carefully, llustrate your answers with examples, Support your answers with mathematics
Provide a comparison of electric / magnetic dipoles and their associated fields, in the case of finite separated charges / finite loop currents respectively. For both electric and magnetic dipoles, identify the scaling limit of an ideal or ‘perfect’ dipole for which the spatial extent becomes infinitesimal, with finite dipole moment.
By considering a scalar potential, describe the relationship between the field lines for an electric versus magnetic dipole, in the above limit, and provide a physical interpretation (including divergence).
Consider a ‘stretched’ magnetic dipole, generated by current flowing in an elongated (rectangular) loop – sketch the field lines compared to those of a finite dipole generated from a circular current loop. Suppose the scaling limit is taken preserving the (elongated) aspect ratio of the loop. What is the relationship between the resulting dipole and that obtained from a circular loop, in this limit?
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