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Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 2 / 16D / a / Solution

The Maxwell equation

\nabla \times E = - \partial B / \partial t

, integrated over a fixed spanning surface

S

, gives by Stokes theorem

\oint_{\partial S} E \cdot d l = - \int_{S} \frac{\partial B}{\partial t} \cdot d S = - \frac{d}{d t} \int_{S} B \cdot d S .

Thus the electromotive force and magnetic flux obey Faraday's law

E = - \frac{d Φ _{B}}{d t} .

Solved by gpt-5.6-sol high.

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