Lenz's Law — Question 5

Question 5

A nearby loop is repelled by a rising source current and attracted by a falling one

A rectangular resistive loop lies to the right of a long vertical wire carrying positive current I upward. Choose out-of-page loop normal. Its external flux is $\Phi=-kI$, with k positive. Ignore self-inductance and hold geometry fixed while determining the response.

1. Find the induced current sense when I increases and when it decreases.

2. Use the near side of the loop to determine the dominant force toward or away from the wire.

Question 5 - Solution

A nearby loop is repelled by a rising source current and attracted by a falling one

(a) Method and calculation

$$\mathcal E=-\dot\Phi=k\dot I,\quad i=k\dot I/R.$$$$\dot I>0:\ i>0\text{ (CCW)};\quad\dot I<0:\ i<0\text{ (CW)}.$$

(b) Interpretation and further calculation

$$\text{CCW near-side current is downward, opposite the wire}\Rightarrow\boxed{\text{repulsion}}.$$$$\text{CW near-side current is upward, parallel to the wire}\Rightarrow\boxed{\text{attraction}}.$$

Physical check

The nearer parallel segment dominates because the source field decreases with distance.