Two Experiments — Question 7

Question 7

Opposed pickup windings distinguish a local source from a common field change

Two equal N-turn pickups of area A are series-connected with opposite winding senses. Their local fields are $B_1=B_c+b$ and $B_2=B_c$, both normal to the coils. Here Bc is a common background and b is a local signal. 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 net linkage and emf.

2. If the second pickup has area $(1+\epsilon)A$, find the residual background contribution and a bound for keeping it below 1 percent of the signal.

Question 7 - Solution

Opposed pickup windings distinguish a local source from a common field change

(a) Method and calculation

$$\Lambda=NA(B_c+b)-NAB_c=NAb.$$$$\boxed{\mathcal E=-NA\dot b}.$$

(b) Interpretation and further calculation

$$\Lambda=NAb-NA\epsilon B_c\Rightarrow\mathcal E=-NA\dot b+NA\epsilon\dot B_c.$$$$\boxed{|\epsilon\dot B_c|\le.0100|\dot b|}.$$

Physical check

The cancellation rejects spatially common changes only to the extent that the two effective pickup areas match.