Halliday, Resnick & Walker — Induction and Inductance: Problem 30

30 Figure 30-33a shows a circuit consisting of an ideal battery with emf \(\mathcal{E} = 6.00 \text{ mV}\), a resistance \(R\), and a small wire loop of area \(5.0 \text{ cm}^2\). For the time interval \(t = 10 \text{ s}\) to \(t = 20 \text{ s}\), an external magnetic field is set up throughout the loop. The field is uniform, its direction is into the page in Fig. 30-33a, and the field magnitude is given by \(B = at\), where \(B\) is in teslas, \(a\) is a constant, and \(t\) is in seconds. Figure 30-33b gives the current \(i\) in the circuit before, during, and after the external field is set up. The vertical axis scale is set by \(i_s = 4.0 \text{ mA}\). Find the constant \(a\) in the equation for the field magnitude.