268 Week 8: Faraday’s Law and Induction
If the conducting loop were decreasing in area (in (b)), the inducedcurrent would be in the
direction that creates a magnetic moment for the loopinthe same direction as the magnetic field
through the loop, againopposing the(now decreasing)change in flux. This direction for the current
also creates a generaloutwarddirected force on all parts of the loop, which would make the loop
growto oppose the decrease in flux.
0.0.2 Lenz’s Law for changingB(magnitude)
I,E I,E(a) (b)R RB(increasing) B(decreasing)Figure 95: Illustration ofE~-field direction when the magnitude ofBthrough the loop changes. In
(a)Bis getting larger (tending to increase the magnetic flux) so the induced magnetic moment
from a counterclockwiseE~field and current opposes the existing field through the loop. In (b)Bis
getting smaller (tending to decrease the flux) so the induced magnetic moment from the clockwise
E~field and current supports the existing field through the loop.
In figure 95 we illustrate what happens when themagnitudeof theB-field changes. In (a),B
is increasing in magnitude through a fixed loop while maintaining a fixed direction. Again if we
imagine a conducting pathway aroundC the (counterclockwise as shown withB~ into the page)
current induced in it would create a magnetic moment from the loop that is in theoppositedirection
asB~, opposing the change in flux. The forces acting on this current in each wire of the loop would
pointinward, trying toshrink the loopas an alternative way of reducing the flux.
In (b),Band the magnetic flux are decreasing in magnitude and the opposite happens – the
induced moment would create anE~-field and associated current that circulate in the (clockwise)
direction such that the induced magnetic momentsupportsdecreasing field (opposing the change in
flux). The magnetic forces on the loop wires would pointoutward, trying toexpand the loopas an
alternative way of increasing the flux.
0.0.3 Lenz’s Law for changingB~ ornˆdirection
Now we imagine the shape of the loopCdoesn’t change, the magnetic field is constant in magnitude,
but the loop’sorientationin the magnetic field could be changingorthedirectionof the magnetic
field could be changing. Note that both have the same effect: they alter theanglebetween the field
and the normal to the plane of the loop, and hence the flux throughthe loop. This is actually a
very common situation – it describes an electrical generator or electrical motor rather well.
IfB~andnˆare rotating into alignment about the dashed line axis shown (decreasingθand hence
increasing cos(theta) and the flux) as shown in (a) of figure 96, the field direction and induced current
areclockwisewhen viewed from above the loop to make the induced magnetic moment opposite to