Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / Section B / 10 / d / Solution

The regular hexagon has area $A=6(\sqrt{3}{a}^2/4)=3\sqrt{3}{a}^2/2$. Choose $t=0$ with its positive normal parallel to the imposed field. The external magnetic flux is $\Phi =B_{0}A\cos \omega t$, so Faraday's law of induction givesTaking the stated resistance to determine the loop response,A different initial orientation adds a phase. The sign is with respect to the chosen loop orientation and obeys Lenz's law; reversal of that orientation reverses the signed current. This expression neglects self-inductance, as in the resistive-loop model.