Two Experiments — Question 5

Question 5

A pickup-voltage integral reconstructs a linkage change without knowing the pulse shape

A resistive pickup records signed emf $\mathcal E(t)=E_0\sin(\pi t/T)$ for $0<t<T$. It is zero outside this interval. Let E0=.200 V, T=.0300 s and R=4.00 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 total linkage change.

2. Find the signed transported charge and explain what remains unknown about the absolute linkage.

Question 5 - Solution

A pickup-voltage integral reconstructs a linkage change without knowing the pulse shape

(a) Method and calculation

$$\Delta\Lambda=-\int_0^T E_0\sin(\pi t/T)dt=-\frac{2E_0T}{\pi}.$$$$\boxed{\Delta\Lambda=-.0120/\pi\,\mathrm{Wb}}.$$

(b) Interpretation and further calculation

$$Q=\frac1R\int_0^T\mathcal E\,dt=\boxed{.00300/\pi\,\mathrm C}.$$$$\Lambda(t)=\Lambda(0)-\int_0^t\mathcal E\,dt\quad\text{contains the unknown constant }\Lambda(0).$$

Physical check

A pickup measures change in flux linkage, not an absolute static flux.