Igcse Model Questions Vol1 2024 Physics Question 3

A single‑turn rectangular coil of width \(L = 0.10\ \text{m}\) and length \(l = 0.15\ \text{m}\) (so the side that enters the field first has length \(l\)) is pulled at constant speed \(v\) into a region where a uniform magnetic field \(B = 0.60\ \text{T}\) points into the page. The coil has \(N = 50\) turns and resistance \(R = 2.0\ \Omega\). (a) While the coil is partially inside the field (i.e., \(0 < x < l\), where \(x\) is the distance the leading edge has entered), derive an expression for the induced emf \(\varepsilon\) as a function of \(x\). (b) Find the maximum speed \(v_{\max}\) that can be used so that the induced emf never exceeds \(5.0\ \text{V}\). (c) Using this speed, calculate the average electrical power dissipated in the coil while the coil is moving from \(x = 0\) to \(x = l\).