Lenz's Law — Question 2

Question 2

An approaching north pole and a receding north pole produce opposite pickup faces

A magnet north pole faces a nearby coil. View the coil from the magnet side and choose positive circulation counterclockwise in that view. Its external flux is modeled by $\Phi=-C/d^3$, where d is separation and C positive. Resistance is R; ignore self-inductance.

1. Find the current sign during approach and recession.

2. Identify the magnetic pole of the coil face nearest the magnet and the direction of its mechanical response in each case.

Question 2 - Solution

An approaching north pole and a receding north pole produce opposite pickup faces

(a) Method and calculation

$$\dot\Phi=3C\dot d/d^4,\quad i=-3C\dot d/(Rd^4).$$$$\dot d<0:\ i>0\text{ (counterclockwise)};\quad\dot d>0:\ i<0\text{ (clockwise)}.$$

(b) Interpretation and further calculation

$$\text{approach: near face N}\Rightarrow\boxed{\text{repulsion}}.$$$$\text{recession: near face S}\Rightarrow\boxed{\text{attraction}}.$$

Physical check

Both responses oppose the relative change in separation. The specified viewing direction is essential for naming clockwise and counterclockwise.