Neco Model Questions Vol1 2023 Physics Question 36

A rectangular conducting loop of resistance \(R = 2\ \Omega\) has horizontal length \(l = 0.20\ \text{m}\) and vertical width \(w = 0.10\ \text{m}\). It is pulled with constant speed \(v\) into a uniform magnetic field of magnitude \(B = 0.50\ \text{T}\) directed into the page. When the leading side just enters the field, an emf \(\mathcal{E}=B l v\) is induced and a current \(I=\mathcal{E}/R\) flows. The magnetic force on the side of length \(l\) inside the field is upward, while the weight of the loop is \(mg\) downward, where the mass of the loop is \(m = 0.050\ \text{kg}\) and \(g = 9.8\ \text{m s}^{-2}\). Determine (i) the speed \(v\) (in \(\text{m s}^{-1}\)) required for the magnetic force to exactly balance the weight, and (ii) the magnitude of the horizontal pulling force \(F\) (in N) needed to keep the loop moving at this speed.