Two Experiments — Question 3

Question 3

Reversing a magnet and reversing its motion have separate sign effects

At a given coil position a north-facing magnet moving right produces linkage slope $d\Lambda/dx=+k$, with k positive. Reversing the magnet changes the entire linkage sign. A positive pickup current is defined by the chosen positive emf. 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 emf for the original passage and for reversing only motion.

2. Find the emf for reversing only magnet polarity and for reversing both polarity and motion.

Question 3 - Solution

Reversing a magnet and reversing its motion have separate sign effects

(a) Method and calculation

$$\mathcal E_{N,+v}=-kv.$$$$\boxed{\mathcal E_{N,-v}=+kv}.$$

(b) Interpretation and further calculation

$$\mathcal E_{S,+v}=-(-k)v=+kv.$$$$\boxed{\mathcal E_{S,-v}=-(-k)(-v)=-kv}.$$

Physical check

Two independent sign reversals restore the original signal, a useful check of pickup wiring and magnet orientation.