physics
Physics 196 VirtuLab: Ampere, Faraday & Lenz
Name:
Lab Day:
Overview
Explore the relationships between cu
ents and magnetic fields and how changes in one produce
changes in the other.
Mathematical Models and Assumptions
Ampere’s Law is a simplified form of the Biot-Savart integral that can be applied when there is a
large amount of symmetry in the system. Much like Gauss’ Law related enclosed charge to the
electric field at the Gaussian surface, Ampere’s Law related the enclosed cu
ent to the
magnetic field at the boundary of the enclosure. ∮ B⃗⋅d⃗l=μ0 I enclosed .
Faraday’s Law relates changes in magnetic flux - ΦB - through a surface to an EMF around the
perimeter of that surface. That EMF will cause a cu
ent to flow around the perimeter. Lenz’s
Law tells us that the induced cu
ent will flow in such a way as to oppose the change in
magnetic flux. ∮ E⃗⋅d⃗l=ϵ=−dΦBdt .
Data Collection: Part One
Visit this URL: https:
www.thephysicsaviary.com/Physics/Programs/Labs/FieldFromWire
Click ‘Begin’ to launch the simulation. You will need to modify
most of the settings before collecting data.
Click ‘Location of the Field Sensor’.
Click ‘Direction’ and select ‘Conventional Cu
ent’.
Click on ‘Cu
ent’.
Click on ‘Field Strength’
Click on ‘Grid’
Part I. Magnetic Field from Cu
ent
When you first start the simulation the magnetic field sensor is in the middle of the grid. Answe
the following questions in the spaces provided, using complete sentences.
Use the ‘Location of the Field Sensor’ a
ow to move the sensor left and right. After each
movement of the sensor wait a few seconds. Describe the effect of this motion on the measured
magnetic field.
© Claude Mona, 2020. Last Edit: 25/01/21 12:34:44
https:
www.thephysicsaviary.com/Physics/Programs/Labs/FieldFromWire
Physics 196 VirtuLab: Ampere, Faraday & Lenz
Use the ‘Location of the Field Sensor’ a
ow to move the sensor towards and away from the
wire. After each movement of the sensor wait a few seconds. Describe the effect of this motion
on the measured magnetic field.
Use the ‘Cu
ent’ a
ows to increase and decrease the cu
ent flowing through the wire. After
each change to the cu
ent wait a few seconds. Describe the effect of these changes on the
measured magnetic field.
Use the ‘Direction’ a
ows to reverse the cu
ent flowing through the wire. After each change to
the cu
ent wait a few seconds. Describe the effect of these changes on the measured magnetic
field.
Now place the sensor at the point (5,5). Set the cu
ent to zero. Record the measured magnetic
field in Data Table One. Increase the cu
ent, and for each new cu
ent value record the
magnitude of the magnetic field. Continue until the data table is complete.
Data Table One
Radial sensor position: 5 centimeters
Cu
ent (A)
Magnetic Field (µT)
Use the data table to construct a Cartesian graph of Measured Magnetic Field as a function of
Cu
ent. Calculate the slope of the best-fit line to your data on the graph, with units.
Now place the sensor at the point (5,1). Set the cu
ent to some non-zero value. Record the
cu
ent and the measured magnetic field in Data Table Two. Move the sensor to (5,2) and record
the measured magnetic field. Continue until the data table is complete.
© Claude Mona, 2020. Last Edit: 25/01/21 12:34:44
Physics 196 VirtuLab: Ampere, Faraday & Lenz
Data Table Two
Cu
ent Magnitude: XXXXXXXXXXAmperes
Position (cm XXXXXXXXXX
Magnetic Field (µT)
How can you tell that your data doesn’t show a linear relationship between measured magnetic
field strength and radial sensor position? Answer using complete sentences in the space below.
In order to ‘straighten out’ the data, can try the form B = Crn. In the space below, start with the
expression for B and take the log10 of both sides. Continue manipulating the expression until you
have a linear expression for the measured magnetic field (B) in terms of the radial position of
the field sensor (r) and the proportionality constant (C). Show/explain each step.
Using a log-log scale, construct a graph of the measured magnetic field strength as a function of
adial sensor position. To simplify analysis, convert centimeters to meters and the magnetic
field strength to Tesla when you plot the data. Notice that the data shows a linear dependence
in this representation. Draw a best-fit line to your data. Calculate the slope of the best fit line
on the graph. Use your data to determine the value of ‘C’ (including units) and record it on the
graph. Use this information to write the equation B = Crn (including proper units) in the space
elow.
© Claude Mona, 2020. Last Edit: 25/01/21 12:34:44
Physics 196 VirtuLab: Ampere, Faraday & Lenz
Ampere’s Law can be used to determine the magnetic field at a radial distance from a long,
straight wire ca
ying a constant cu
ent. Starting with Ampere’s Law and a diagram show that
this becomes B (r )=
μ0
2Ï€
I
.
Use the slope of your graph of measured magnetic field as a function of cu
ent to determine an
experimental value for µ0, with units. Show your work in the space below. Record the result in
Data Table Three as µ0: B v I.
Use the proportionality constant C from your graph of measured magnetic field as a function of
adial sensor distance to determine an experimental value for µ0, with units. Show your work in
the space below. Record the result in Data Table Three as µ0: B v r.
Data Table Three
µ0: B v I
µ0: B v
© Claude Mona, 2020. Last Edit: 25/01/21 12:34:44
Physics 196 VirtuLab: Ampere, Faraday & Lenz
Calculate the percent difference between your experimental results. Calculate the percent
e
or between the average of your values and the accepted value of µ0. Show all work with units
in the space below.
Data Collection: Part Two
Visit this URL:http:
www.thephysicsaviary.com/Physics/Programs/Labs/InducedCu
entLa
Click ‘Begin’ to launch the simulation.
Click ‘Click here to start the tractor moving’ and a tractor will
slide a conducting bar across a set of conducting rails. By
changing the effective area of the loop, magnetic flux is
changing. This leads to an induced EMF and an induced
cu
ent. When there is a cu
ent flowing in the system, the
lightbulb at the end of the loop will light up.
NOTE: This simulation shows the direction of the electron
motion in the circuit. The conventional cu
ent of positive
charge ca
iers will flow in exactly the opposite direction as
the cu
ent a
ow displayed in the simulation.
Part II. Changing Magnetic Flux and Induced Cu
ents
Do not adjust any of the parameters. The tractor should be facing to the left. Reload the
simulation if necessary. The following questions are designed to test your intuition about
Faraday/Lenz scenarios and to help reveal any misconceptions.
When the tractor pushes the bar to the left, the magnetic flux through the area bounded by the
ails and the bar will...(increase or decrease). Write your response below.
Since the induced field will work to oppose any changes in flux, the induced field will point...
(into or out of) the page. Write your response below.
To have an induced magnetic field, there must be an induced cu
ent. This cu
ent will flow
around the loop in a...(clockwise or counterclockwise) direction. Write your response below.
In order to have a cu
ent flow through the bar, there must be an EMF. The ...(top or bottom) of
the bar is at a higher potential than the other end. Write your answer below.
© Claude Mona, 2020. Last Edit: 25/01/21 12:34:44
http:
www.thephysicsaviary.com/Physics/Programs/Labs/InducedCu
entLa
Physics 196 VirtuLab: Ampere, Faraday & Lenz
Now activate the tractor and look at the direction of the green a
ow near the lightbulb.
Recalling the direction difference between the actual and conventional cu
ent, are your
answers consistent with the results of the simulation? On the following page, record any of your
predictions that were invalid.
Next, complete the scenarios in the Predicted Data Table Four and predict whether the
magnitude and direction of the induced cu
ent will increase, decrease or stay the same.
Predicted Data Table Fou
If I…
…then the cu
ent will
(increase/decrease, stay the
same)…
…and the direction of the
cu
ent will (reverse/stay
the same).
Reverse the direction
of velocity...
Reverse the direction
of magnetic field...
Increase the magnetic
field...
Increase the rail
separation...
Increase the circuit
esistance...
Once you have predicted the outcomes, vary the appropriate input and verify or disprove your
predictions. Were there any of your predictions that were inco
ect? What was the flaw in your
easoning that led you to make an inco
ect prediction? Answer using complete sentences in the
space below.
© Claude Mona, 2020. Last Edit: 25/01/21 12:34:44
Physics 196 VirtuLab: Ampere, Faraday & Lenz
Now it is time to take some data. Record the magnitude of the magnetic field, rail separation
and circuit resistance in Data Table Five. Start the tractor moving, then click ‘Pause’ after it has
moved about 10 centimeters. Determine the final position as accurately as possible and record
this value and the elapsed time in the data table.
Data Table Five
Magnetic Field
(mT)
Circuit Resistance
(Ω)
Initial Position
(cm)
Induced Cu
ent
(mA)
0
Rail Separation
(mm)
Elapsed Time
(ms)
Final Position
(cm)
Using constant velocity kinematics, calculate the average speed of the tractor and rail. Show all
work with units in the space below. Label the result as