A rectangular conducting loop of width $0.50$ m and length $0.50$ m is pulled at constant speed into a region where the magnetic field varies with distance $x$ as $B(x)=0.50\,\text{T}\,(1-\frac{x}{0.50})$ for $0\le x\le0.50$ m and is zero elsewhere. The loop resistance is $R=1\,\Omega$. The loop starts outside the field and is moved until it is completely inside.\
(a) Find the speed $v$ such that the total energy dissipated as heat during the entry process is $0.5$ J.\
(b) Using that speed, determine the maximum induced emf in the loop.\
(c) What is the total energy dissipated as heat during the whole process of entering and then leaving the field?

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v = 48 m·s⁻¹, ε_max = 12 V, total energy = 1 J

Neco Model Questions Vol1 2024 Physics Question 46

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