phy1020.DVI

R

I

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Figure 36.1: Motional emf.

Lenz’s law(named for the 19th century Russian physicist Heinrich Lenz):

The emf and induced current are in such a direction as to tend to oppose the change which

produced them.

36.2 Motional EMF

As an example to illustrate both Faraday’s law and Lenz’s law, consider the situation shown in Figure 36.1.
Two parallel conducting rails separated by a distancelare connected on their left end by a resistor. A
conducting bar is placed across the rails, and the entire apparatus is placed in a uniform magnetic fieldB
pointing into the page. Now move the conducting rail to the right with velocityv; this will increase the area
enclosed by the circuit, which will increase the magnetic flux inside the circuit. By Faraday’s law, this will
induce an electromotive force (voltage) in the circuit. An emf induced in this way is calledmotional emf.
We can find the magnitude of the induced emf using Faraday’s law. At a given instant, there is an areaA
enclosed by the circuit, formed by the rails, resistor, and conducting bar. When the bar is moving at velocity
vto the right, then in a time intervaltthe area increases by an amountlvt. The rate at which the area
changes is then

A

t

D

lvt

T

Dlv: (36.2)

Since the magnetic fluxˆBDBA,wehave

ˆB

t

DB

A

t

DBlv: (36.3)

Therefore by Faraday’s law, the magnitude of the induced electromotive force is

jEjD

ˆB

t

DBlv: (36.4)

We can deduce thedirectionof the induced current by using Lenz’s law, which says that the induced
current must be in such a direction that the magnetic field it produces will tend to oppose the change in
magnetic flux. If the conducting bar moves to the right, then the magnetic fluxˆBisincreasingwith time.
Therefore the induced current must becounterclockwise, because, by the right-hand rule, a counterclockwise