Neco Model Questions Vol1 2017 Physics Question 9

A long solenoid of length \(0.50\ \text{m}\) has \(800\) turns and a radius of \(2.0\ \text{cm}\). The current through the solenoid varies with time as \(I(t) = 2 t^{2}\ \text{A}\) (where \(t\) is in seconds). (a) Write an expression for the magnetic field inside the solenoid as a function of \(t\). (b) At \(t = 3\ \text{s}\) the current is switched off instantaneously. During the first \(0.01\ \text{s}\) after switch‑off, a single circular loop of radius \(3.0\ \text{cm}\) placed coaxially at the centre of the solenoid experiences an induced emf. Assuming the loop's resistance is \(5\ \Omega\), calculate the energy dissipated as heat in the loop during this interval (express your answer in scientific notation with two significant figures).