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2nd Year Electromagnetism Part 1: Assessed Problem

Due Wednesday 31st January 2024, 4 p.m.

1   APS Assessed problem: Currents on superconductors

An ininite plane current sheet, ininitesimally thin, carries a uniform current I per unit length.

•  (i) Show that the component of the magnetic ield which is perpendicular to the sheet normal, and parallel to I is continuous across the sheet. [5 marks]

•  (ii) Calculate the magnetic ield everywhere. [5 marks]

A superconductor has zero magnetic ield inside it, but allows currents to low on its surface. An ininite plane sheet of ma甘er, of inite thickness L, is placed in a uniform magnetic ield B, such that the ield is perpendicular to the sheet normal. It is cooled down until it becomes superconducting.

•  (iii) Work out the current per unit length that must low on the surfaces to remove the magnetic ield inside it. [5 marks]