Lenz's Law — Question 8

Question 8

Coplanar separated coils can induce currents with the same circulation sense

Two small coils lie far apart in the same xy plane. The source moment is along +z and increases in magnitude. At the pickup, the source dipole field is along -z. Choose pickup normal +z and use its calibrated flux $\Phi_2=-kI_1$, k positive. Its resistance is R.

1. Find pickup current during increasing positive I1.

2. Compare with a coaxial pickup on the positive z axis, whose calibration is $\Phi_2=+kI_1$.

Question 8 - Solution

Coplanar separated coils can induce currents with the same circulation sense

(a) Method and calculation

$$\mathcal E_{\mathrm{coplanar}}=+k\dot I_1,\quad\boxed{i_{\mathrm{coplanar}}=+k\dot I_1/R}.$$$$\dot I_1>0:\quad\vec\mu_2\parallel+\hat z\text{, the same sense as the source}.$$

(b) Interpretation and further calculation

$$\mathcal E_{\mathrm{coaxial}}=-k\dot I_1,\quad\boxed{i_{\mathrm{coaxial}}=-k\dot I_1/R}.$$$$\vec\mu_2\parallel-\hat z\quad\text{for increasing positive source current}.$$

Physical check

Lenz law opposes the local flux change; it does not require every induced loop to oppose the source loop magnetic moment.