Section 5.3 · Home exercises · 1 of 2
Home exercise 5.3.1: Circular loop in a changing field
Circular loop in a changing field
#A circular wire loop of radius lies on the -plane in the uniform field .
- Find the electromotive force induced in the loop.
- The loop has a total resistance . Find the induced current and state, with Lenz's law, in which sense it flows while is increasing.
Adapted from: D. K. Cheng, Field and Wave Electromagnetics, 2nd ed., Example 7-1.
The loop is at rest, so only the transformer term is present and with the flux of a uniform field through a flat disc, . The sign of follows from the right-hand rule and is confirmed by Lenz's law.
Take . The field is uniform over the loop, so
The reference sense of is the one that goes with by the right-hand rule: counter-clockwise seen from .
With the loop closed through its own resistance,
While is increasing (, for instance ) the current is negative in the counter-clockwise reference, that is it flows clockwise seen from . A clockwise current produces, by the right-hand rule, a field along inside the loop, opposing the growth of , as Lenz's law demands. During the next quarter period decreases and the current reverses, now trying to keep the flux up.
Set cm, T, Hz and read the peak emf.
The peak emf is : for , at it is . Units: . The induced current itself produces a small flux through the loop (the self-inductance of Chapter 4). Neglecting it is justified when .