Two Experiments — Question 4

Question 4

A stationary strong field produces no sustained pickup current

A fixed source coil has current $I_1(t)$ that rises linearly from zero to 2.00 A in .0100 s, remains constant for .100 s, then falls linearly to zero in .0400 s. Its linkage calibration is k=.00300 Wb/A and pickup resistance is 5.00 ohms. For this calibrated experiment, use signed flux linkage $\Lambda=N\Phi$, $\mathcal E=-d\Lambda/dt$ and $i=\mathcal E/R$; neglect pickup self-inductance.

1. Find the pickup emf and current during each of the three intervals.

2. Find the signed charge during the rise and fall and their sum.

Question 4 - Solution

A stationary strong field produces no sustained pickup current

(a) Method and calculation

$$\mathcal E=-k\dot I_1:\quad\boxed{\mathcal E_{\mathrm{rise}}=-.600\,V,\ \mathcal E_{\mathrm{hold}}=0,\ \mathcal E_{\mathrm{fall}}=+.150\,V}.$$$$\boxed{i_{\mathrm{rise}}=-.120\,A,\quad i_{\mathrm{hold}}=0,\quad i_{\mathrm{fall}}=+.0300\,A}.$$

(b) Interpretation and further calculation

$$Q_{\mathrm{rise}}=-.120(.0100)=-1.20\,\mathrm{mC},\quad Q_{\mathrm{fall}}=.0300(.0400)=+1.20\,\mathrm{mC}.$$$$\boxed{Q_{\mathrm{total}}=0}.$$

Physical check

The steady hold has a nonzero magnetic field but zero linkage derivative.