Two Experiments — Question 1

Question 1

Equal flux histories connect the moving-magnet and switched-current experiments

Experiment A moves a magnet so that pickup linkage is $\Lambda_A=\Lambda_0e^{-t/T}$. Experiment B holds both coils fixed and uses source current $I_1=I_0e^{-t/T}$ with pickup calibration $\Lambda_B=kI_1$. 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 condition for identical pickup signals and their time dependence.

2. For linkage amplitude .0120 Wb, T=.0400 s and R=6.00 ohms, find initial emf and current.

Question 1 - Solution

Equal flux histories connect the moving-magnet and switched-current experiments

(a) Method and calculation

$$\mathcal E_A=\frac{\Lambda_0}{T}e^{-t/T},\quad\mathcal E_B=\frac{kI_0}{T}e^{-t/T}.$$$$\boxed{kI_0=\Lambda_0\Rightarrow\mathcal E_A(t)=\mathcal E_B(t)}.$$

(b) Interpretation and further calculation

$$\mathcal E(0)=.0120/.0400=\boxed{.300\,\mathrm V}.$$$$i(0)=.300/6.00=\boxed{.0500\,\mathrm A}.$$

Physical check

The pickup responds to changing linkage; its signal alone does not identify whether motion or source-current variation produced that change.