Conceptual Physics

(Sean Pound) #1

Ǜ = í(6 loops)(0.15 V) = í0.90 V


29.8 - Interactive problem: Faraday’s law


In this simulation, a magnetic field is passing through a solenoid. The solenoid is
part of a circuit that contains a resistor. The potential difference across the resistor
equals the magnitude of any emf induced in the solenoid.


You control the rate of change of the magnetic field passing through the solenoid.
Your task is to use Faraday’s law to calculate the time rate of change of magnetic
flux through the solenoid that will induce an emf having a magnitude of 12.5 V and
cause current to flow in the circuit. In turn, this will create a potential difference of
12.5 V across the resistor.


The solenoid has 20 loops, and each loop has an area of 0.0100 m^2. An
oscilloscope measures the potential difference across the resistor.


The magnetic field starts at 0.500 T and will decline linearly to 0 T during a time
interval you specify. You have a controller that sets the time interval during which
the change in field strength will occur to values from 5.00 to 20.00 milliseconds. The
field will then continue to vary back and forth between 0 T and 0.500 T during
alternating time intervals of the same length. The rate of change will alternate
between positive and negative values, but it will have a constant magnitude based on the duration of the time interval you select.


Specify the time during which you want the field to decline to zero. (You change it in increments of 0.10 milliseconds.) Press GO to see if the
changing field induces an emf of magnitude 12.5 volts. If not, press RESET, redo your calculations and try again.


If you have trouble answering this problem, review the section on Faraday’s law. The oscilloscope displays a graph of the potential difference
across the resistor, with the potential difference plotted on the vertical axis and elapsed time on the horizontal axis. By clicking on different
values on the oscilloscope’s control knob, you can specify what you want the vertical measure, in volts, of one grid square to be.


29.9 - Lenz’s law


Lenz’s law: An induced current flows so that


the magnetic field it creates opposes the change


in magnetic flux that causes the current.


Lenz’s law, named after the Russian scientist Heinrich Lenz (1804-1865), is used to
determine the orientation of the current induced by a change in magnetic flux.


The law states that the magnetic field of the induced current opposes the change in
magnetic flux that causes the current. To apply the law, you first note the change in
magnetic flux and then determine the orientation of the magnetic field that will oppose
that change in flux. The current will flow in the direction that causes this magnetic field.


To illustrate this law being applied, we use the wire loop shown to the right. The
external magnetic field is pointing into the page and it is increasing in strength. This will
cause a current. But in which direction does the current flow, clockwise or counterclockwise?


To answer this question, consider the direction of the magnetic field created by the induced current. Lenz’s law says this field will oppose the
change that caused it. The external field is increasing, so the magnetic field of the induced current points in the direction that opposes this
change. This means it will point toward you, as the diagram in Concept 2 shows. (In this diagram we have dimmed the external field to make
the opposing field easier to see.)


The right-hand rule for currents dictates that the current must be flowing counterclockwise through the wire loop. If you apply the rule, your
fingers inside the loop must point toward you, opposing the increase of the external magnetic flux that is pointing away from you. This means
the thumb points up on the right side of the loop, as illustrated in Concept 2, and down on the left side, as you can imagine, indicating the
direction of conventional current. “Up on the right” and “down on the left,” means the current flows counterclockwise.


(Perhaps it is useful to state a right-hand rule for induction loops: “The thumb points in the direction of the induced magnetic field, and the
fingers wrap around the loop to indicate the direction of the current.”)


If the external field were decreasing, then the induced magnetic field would oppose the decrease. It would point in the same direction as the
external field, and this means the current would flow clockwise.


The example problem asks you to determine the direction of the current in a loop when a decreasing external magnetic field passes through it,


Lenz’s law


Determines direction of induced current


Copyright 2007 Kinetic Books Co. Chapter 29^545

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