Electric Fields
Electric Fields Tutorial
Jeanne Morse 2002
Some pages of this tutorial contain Physlets developed by Dr. Wolfgang Christian at
Davidson College. The author is grateful to Dr. Christian for making the Physlets available to physics teachers.
Three of the practice problems on this tutorial are based on parts of a problem from
Randal Harrington's dissertation (Randal Robert Harrington, Ph.D. dissertation, University of Washington, 1995). They are: Practice problem 10 of the section "Electrostatic force on a charge", Practice problem 2 of the section "Finding the electric field at a point", and Practice problem 5 of the section "Finding the electric field at a point".
Welcome to the Electric Fields Tutorial program. The program reviews a set of concepts that are important in understanding electric fields.
You will review
● how to use a vector to represent the electric field
● how the force on a charged particle is related to the electric field. ● how to find the electric field at a point
You should already know
● what an electric charge is.
● the units used to measure electric charge.
● that electric fields exist around charged objects. ● the units used to measure electric field
You will need a calculator, paper, and a pencil or pen.
Click here to start the Electric Fields Tutorial.
Introduction
Introduction
The tutorial runs as a Web page. It runs in Internet Explorer 5.0 or higher, or Netscape 4.77 or higher.
The tutorial contains review material and practice problems. Review material appears on pages like this one.
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/intro_01.htm6/13/2005 8:08:14 PM
Practice problems appear on pages like this one. Some of the problems require a calculator.
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/intro_02.htm6/13/2005 8:08:48 PM
Introduction
Some pages contain Java applets. Applets are used to illustrate concepts and as part of some practice problems.
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/intro_03.htm6/13/2005 8:09:01 PM
Contents
Select a topic to review and click "Continue". Using vectors to represent the electric field Electrostatic force on a charge
Finding the electric field at a point
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/contents.htm6/13/2005 8:09:41 PM
Using vectors to represent the electric field Using vectors to
represent the electric field
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/representing_E/opening_page_layout.htm6/13/2005 8:10:28 PM page 1 of 12
You've learned in class that electric fields have magnitudes and directions.
The electric field has a magnitude and a direction at each point in space, just as each point in space has a
temperature. The temperature at different locations can be represented by numbers as you see on weather maps. The only way to show both the magnitude and direction of the electric field on diagrams is to use a vector.
Go to Contents
Using vectors to represent the electric field
Numbers aren't enough
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/representing_E/efo~1.htm6/13/2005 8:13:38 PM page 3 of 12
The vectors in this figure represent the electric field at different locations.
Electric field vectors.
The relative lengths of the vectors in the figure tell you that the electric field is strongest at the lower right and weakest at the upper left.
There are conventions for drawing electric fields. You need to know these conventions to understand the vector
diagrams. Go to Contents
Using vectors to represent the electric field
Using vectors to represent the electric field
Numbers aren't enough
You need vectors
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/representing_E/efo~3.htm6/13/2005 8:15:25 PM page 4 of 12
To draw a vector you need to know three things.
Where do you put the tail of the vector?
What direction does the vector point?
How long should the vector be?
You probably already know that the vector points in the direction of the electric field. Before you can draw the vector, though, you have to know where to start drawing.
Go to Contents
Using vectors to represent the electric field
Numbers aren't enough
You need vectors
Where does the tail go?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/representing_E/page_05_layout.htm (1 of 2)6/13/2005 8:19:16 PM page 5 of 12
Joe missed class and borrowed Larry's notes to copy. Joe: I can't figure out what this drawing is about.
Larry's drawing
Larry: I copied that off the board. The vectors show the electric field at A and B. The field's larger at A so the vector's longer.
Joe: Phil's got this in his notes.
Phil's drawing
He has the vectors starting at A and B, and you've got the vectors with A and B at the end.
Larry: I guess it's the same thing. I mean, they're the right length, and they're pointing the right way.
Joe: Do you think it'll make a difference, like, on a test? What do you think? Does it matter where the vector is drawn?
Yes No.
Using vectors to represent the electric field
It does matter where you draw the vector.
An electric field vector represents the electric field at a specific point. The tail of the vector is placed at that point. (You'll see why when you do the section "Finding the electric field".) Larry didn't draw the electric field vectors with the tails at A and B, so Larry's sketch doesn't tell you anything about the electric field at A or B.
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/representing_E/page_05_layout.htm (2 of 2)6/13/2005 8:19:16 PM Vectors just have magnitude and direction.
Submit
Using vectors to represent the electric field
Numbers aren't enough
You need vectors
Where does the tail go?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/representing_E/page_05a_layout.htm6/13/2005 8:20:17 PM page 6 of 12
You move force vectors around when you draw free body diagrams.
Why can't you do the same thing with electric field vectors? The electric field at a location is related to the force on a charge placed at that location. The electric field vector represents the field at that location.
The magnitude of the force, or its direction, or both, will be different at each location. That makes the electric field
different as well. This is why electric field vectors have to be drawn at a specific location.
right wrong
Can I still move vectors to add them?
Go to Contents
Using vectors to represent the electric field Using vectors to
represent the electric field
Numbers aren't enough
You need vectors
Tail is at
location field is known
What's the length?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/representing_E/page_06_layout.htm6/13/2005 8:21:42 PM page 7 of 20
Drag the "x" to see the electric field vector at different points.
The simulation lets you see how the length of the electric field vector changes when |E| changes. Is the length of the vector directly proportional to |E|?
Yes No
How can you tell? Go to Contents
Its length doubles when the field doubles.
Using vectors to represent the electric field
Numbers aren't enough
You need vectors
Vector points in direction of |E|
Tail is at
location field is known
Length of vector α |E|
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/representing_E/efo~3.htm6/14/2005 9:03:08 AM page 8 of 12
Practice problem
The electric field at point A points straight up (toward the top of the screen). It has a magnitude of 20 N/C. Use the mouse to draw a vector representing the electric field at point A.
Using vectors to represent the electric field
Using vectors to represent the electric field
Numbers aren't enough
You need vectors
Vector points in direction of |E|
Tail is at
location field is known
Length of vector α |E|
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/representing_E/efo~5.htm6/14/2005 9:06:14 AM page 9 of 12
Practice problem
The table gives the electric field at several different locations. Use the mouse to draw vectors representing the electric field at these points.
location |E| direction of E
A 7 up
B 10 left
C 3 right
Using vectors to represent the electric field
Numbers aren't enough
You need vectors
Vector points in direction of |E|
Tail is at
location field is known
Length of vector α |E|
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/representing_E/prob_03_layout.htm6/13/2005 8:26:37 PM page 10 of 12
Practice problem
The figure shows electric field vectors at 3 locations.
One square=2 N/C
You know that |EA|=6 N/C, |EB|=5 N/C, and |EC|=8 N/C. The electric field points toward the bottom of the screen. Which vector(s) is(are) not drawn correctly? Check all that apply.
A B C
All the vectors are drawn correctly. Go to Contents
Using vectors to represent the electric field Using vectors to
represent the electric field
Numbers aren't enough
You need vectors
Vector points in direction of |E|
Tail is at
location field is known
Length of vector α |E|
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/representing_E/prob_04_layout.htm6/13/2005 8:28:58 PM page 11 of 12
Practice problem
The figure shows some electric field vectors.
Rank the electric field at each point from strongest to
weakest. Use only the symbols ">" and "=" in your answer. Do not use spaces or parantheses in your answer.
Using vectors to represent the electric field
Numbers aren't enough
You need vectors
Vector points in direction of |E|
Tail is at
location field is known
Length of vector α |E|
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/representing_E/end_layout.htm6/13/2005 8:29:30 PM page 12 of 12
You have finished the section on using vectors to represent the electric field. You may go to another section or close the browser to end this session.
Go to Contents
Force on a charge in an external electric field What does
Fon q = qEext mean?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/opening_page_layout.htm6/13/2005 8:29:47 PM page 1 of 19
In class you've learned that
gives the force on a charged particle placed in an electric field. Your book may write this as
.
Let's take a closer look at what the equation tells you.
Go to Contents
Force on a charge placed in an electric field
A closer look at
Fon q=qEext.
Does Eext depend on q?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/page_02_layout.htm6/13/2005 8:30:17 PM page 2 of 19
ext
Eext, or is Eext produced by charges other than q?
Eext is produced by q. Eext is not produced by q..
How did you decide?
Go to Contents
Charges can't apply force to themselves
Force on a charge placed in an electric field Force on a charge
placed in an electric field
A closer look at
Fon q=qEext.
Does Eext depend on q?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/page_03_layout.htm6/13/2005 8:30:40 PM page 3 of 19
Suppose you take q out of the electric field. What happens to the external electric field?
Go to Contents
nothing
Force on a charge placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/page_04_layout.htm6/13/2005 8:31:43 PM page 4 of 19
The simulation lets you see the effects of different electric fields on different charges. Use the sliders to change |E|, the direction of the electric field, and q.
Are electric field and force the same thing? Yes
No
How can you tell? Go to Contents
They aren't always in the same direction.
Force on a charge placed in an electric field Force on a charge
placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
How does F
depend on q?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/page_05_layout.htm6/13/2005 8:32:33 PM page 5 of 19
The simulation lets you see the effects of different electric fields on different charges. Use the sliders to change |E|, the direction of the electric field, and q.
Is |Fon q| directly proportional
to |q|?
How to tell if |Fon q| is directly
proportional to |q|.
Yes No.
How can you tell? Go to Contents
Doubling the charge doubles the force.
Force on a charge placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q|α |q|
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/prob_01_layout.htm6/13/2005 8:32:50 PM page 6 of 19
Practice problem
A 3.5 x 10-12 C charge is placed in a 450 N/C electric field. What is the magnitude of the force on the charge?
N
Note: 1.5 x 10-6 should be entered as 1.5e-6 or 1.5E-6.
Go to Contents
Force on a charge placed in an electric field Force on a charge
placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q|α |q|
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/prob_02_layout.htm6/13/2005 8:34:23 PM page 7 of 19
Practice problem
The force on a charge placed in an electric field is 7.5 x 10 -12 N. The charge is now tripled. What is the force on the charge?
N
Note: 1.5 x 10-6 should be entered as 1.5e-6 or 1.5E-6.
2.25 x 10-11 N is correct. |Fon
q| is directly proportional to |
q|, so tripling q should triple |Fon q|. Go to Contents
22.5e-12 Submit
Force on a charge placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q| α q
How does |Fon q|
depend on |Eext|?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/page_06_layout.htm6/13/2005 8:34:53 PM page 8 of 19
The simulation lets you see the effects of different electric fields on different charges. Use the sliders to change |E|, the direction of the electric field, and q.
Is |Fon q| directly proportional
to |Eext|?
How to tell if |Fon q| is directly
proportional to |E|.
Yes No.
How can you tell? Go to Contents
Doubling E doubles F.
Force on a charge placed in an electric field Force on a charge
placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q| α q
|Fon q| α |Eext|
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/prob_03_layout.htm6/13/2005 8:35:18 PM page 9 of 19
Practice problem
The force on a particle placed in an electric field is 1.6 x 10 -8 N. The electric field is then halved. What is the force on the particle?
N
Note: 1.5 x 10-6 should be entered as 1.5e-6 or 1.5E-6.
8.0 x 10-9 N is correct. |Fon
q| is directly proportional to |
Eext|, so halving |Eext| should halve |Fon q|. Go to Contents
.8e-8 Submit
Force on a charge placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q| α q
|Fon q| α |Eext|
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/prob_04_layout.htm6/13/2005 8:35:41 PM page 10 of 19
Practice problem
The magnitude of the electric field at point A is 4.0 x 10-9 N. The magnitude of the electric field at B is 3.0 x 10-10 N. A positive charge is placed at point A and then moved to point B. At which location will the force on the charge be the
smallest?
The force is smallest at A. The force is smallest at B.
There is not enough information to tell where the force is smallest. You need to know
B is correct.
|Fon q| is directly proportional to |Eext|. |Fon q| will be
smallest where |Eext| is smallest. The electric field at B has a smaller magnitude than at A, so the force on a positive charge will be smaller at B than at A.
Note that you don't have to know what the charge is to tell where the force on the charge is smallest.
Go to Contents
Submit
Force on a charge placed in an electric field Force on a charge
placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q| α q
|Fon q| α |Eext|
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/prob_05_layout.htm (1 of 2)6/13/2005 8:36:57 PM page 11 of 19
Practice problem
The figure shows the electric field vector at several
locations. You put the same positive charge at each location and measure the force on it.
At which location(s) would the force on a positive charge be largest?
A. B. C. D.
There is not enough information to tell where the force is largest. You need to know
B is correct. The electric field vector at B is longer than any others. That indicates that the electric field at B is larger than the electric field at the other three points. Since |Fon q| is directly proportional to |Eext|, the force on a positive
charge will be largest where the electric field is largest. Note that you don't have to know what the charge is to tell where the force on the charge is largest.
Go to Contents ✔
Force on a charge in an external electric field Force on a charge
placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q| α q
|Fon q| α |Eext|
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/page_07_layout.htm6/13/2005 8:37:45 PM page 12 of 19
So far you've seen that
● electric field and electrostatic force are not the same thing.
● Eext is not produced by q.
● |Fon
q| is directly proportional to |q|.
● |Fon
q| is directly proportional to |Eext|.
We've been ignoring the fact that force and electric field both have directions. It's time to find out what determines the direction of the force on a charge placed in an electric field.
Go to Contents
Force on a charge placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q| α q
|Fon q| α |Eext|
What direction is
Fon q?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/page_08_layout.htm6/13/2005 8:38:13 PM page 13 of 19
The simulation lets you see the effects of different electric fields on different charges. Use the sliders to change |E|, the direction of the electric field, and q.
When are Fon q and Eext in the same direction?
When q is negative. When q is positive.
When q and Eext have the same sign. When q and Eext have opposite signs. Go to Contents ✔
Force on a charge placed in an electric field
Force on a charge placed in an electric field
A closer look at Fon q=qEext.
Eext is
independent of q.
|Fon q| αq
|Fon q| α |Eext|
What direction is Fon q?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/prob_06_layout.htm6/13/2005 8:38:40 PM
page 14 of 19
Practice problem
The figure shows the force on a charge placed in an electric field.
Which figure best shows the force on the charge if the electric field is tripled?
A. B. C.
Tripling the electric field triples the force, so the force vector should be three times as long. The correct answer is B.
Go to Contents
Submit
Force on a charge placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q| α q
|Fon q| α |Eext|
What direction is
Fon q?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/prob_07_layout.htm6/13/2005 8:38:59 PM page 15 of 19
Practice problem
The figure shows the force on a positive charge placed in an electric field.
Click on the number that best represents the direction of the electric field that produced this force.
6 is correct. q is positive. When you multiply Eext by a
positive number, the result is a vector in the same direction as Eext. So, Fon q is in the same direction as Eext.
Go to Contents
Force on a charge placed in an electric field Force on a charge
placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q| α q
|Fon q| α |Eext|
What direction is
Fon q?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/efo~9.htm6/14/2005 9:19:20 AM page 16 of 19
Practice problem
The white box shows a negative charge placed in an area where there is an electric field. Select the electric field
direction that will cause the charge to move along the green line. The electric field will be turned on when you make your selection.
Click on the arrow to select the direction of the electric field
Click "reset" to return to the initial conditions.
Go to Contents
pause reset
Force on a charge placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q| α q
|Fon q| α |Eext|
What direction is
Fon q?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/efo~11.htm6/14/2005 9:21:34 AM page 17 of 19
Practice problem
The simulation shows a negative charge moving to the right. Select an electric field direction that will cause the charge to slow down and reverse direction. The electric field will be turned on when you make your selection.
Click on the arrow to select the direction of the electric field
Click "reset" to return to the initial conditions. "pause" will stop the animation, and "play" starts the
animation after it is paused.
Go to Contents
reset pause play
Force on a charge placed in an electric field
Force on a charge placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q| α q
|Fon q| α |Eext|
What direction is
Fon q?
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/prob_10_layout.htm (1 of 2)6/13/2005 8:41:55 PM page 18 of 19
Practice problem
Joe and Sue can't agree on the answer to this homework problem.
You put a 3 nC charge in an electric field and measure the force on it. You then remove the 3 nC charge and replace it with an 18 nC charge. Is the force on the 18 nC charge larger than,
smaller than, or the same as the force on the 3 nC charge? Explain your answer.
Joe: "Force is kqq/r2 so if q increases the force goes up." Sue: "k(q1q2)/r2 is the force between two charges. There aren't two charges here. This is a charge in an electric field. The electric field is what pushes on the 3 nC charge, so you've got to use force is qE. Increasing q makes the force larger."
Whose explanation is better, Joe's or Sue's? Why?
Sue's answer to this question is better than Joe's answer. Joe is using Coulomb's Law, |Fq1->q2| = k(q1q2)/r2, to answer the question. Coulomb's law tells you the force
applied to one charge by another charge. This question does not ask about the interaction between two charges, so
Coulomb's law is not a good way to answer the question. This question asks about charges placed in an electric field. It is better to use Fon q=q Eext to answer the question. The Go to Contents
Sue's. Joe is relying on Coulomb's law.
Force on a charge placed in an electric field
charge is tripled, Eext doesn't change, so Fon q must triple. This is how Sue answered the question. Her reasoning is like this:
Fon q=q Eext, so Fon 3q=3(q Eext)=3(Fon q).
Force on a charge placed in an electric field
A closer look at
Fon q=qEext.
Eext is
independent of q.
|Fon q| α q
|Fon q| α |Eext|
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/force_on_charge/end_layout.htm6/13/2005 8:42:12 PM page 19 of 19
. You saw that
● force and electric field are not the same thing.
● Eext is not the electric field produced by q. It is created by other charges.
● |Fon
q| is directly proportional to |q|.
● |Fon
q| is directly proportional to |Eext|.
● The direction of Fon
q is
the same as the direction of Eext when q is positive.
opposite of the direction of Eext when q is negative.
You can return to the Table of Contents to review another topic or close the browser to end this session.
Go to Contents
Finding the electric field at a point Finding the electric field at a point
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/opening_page_layout.htm6/13/2005 8:42:28 PM page 1 of 16
You've learned in class that the electric field of a point charge can be calculated from
|E| = k q r2
It is easy to find the electric field near one charge. Finding the electric field gets harder when there is more than one point charge to deal with. How would you find the electric field at the "x" in this situation?
It can be very difficult to find the electric field near charged objects like rods or plates because you have to find a way to add up the effects of every charge on the object. The end result is often an integral that you may or may not be able to do.
There is an easier way to find the electric field at a point. Go to Contents
Finding the electric field at a point
E=Fon q/q
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/page_02_layout.htm6/13/2005 8:42:41 PM page 2 of 16
E =
Fon q
q
This should look familiar. Electric fields apply forces to charges, so if we can measure the force on a charge, we should be able to find the electric field at the location of the charge.
The italics are important. This method tells us only what the electric field is at one place: the place we put the charge q.
To find E at the "x",
put a charge, q, on the "x" and measure Fon q
To find the electric field at the "x" all we have to do is put a point charge, q, at the "x", measure the force on q, and divide the force by q to find E.
Go to Contents
Finding the electric field at a point Finding the electric field at a point
E=Fon q/q
Pick q.
Measure Fon q/q.
Calculate E.
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/page_03_layout.htm6/13/2005 8:42:52 PM page 3 of 16
How do you use
E =
Fon q
q to find the electric field?
All you have to do is
● Put a charge in the electric field.
● Measure the force on the charge.
● Divide the force by the charge to get the electric field. This works as long as you use the right charge.
Go to Contents
Finding the electric field at a point
E=Fon q/q
Pick q.
Measure Fon q/q.
Calculate E.
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/page_04_layout.htm6/13/2005 8:43:31 PM page 4 of 16
"Electric field is kq/r2, but it's also (F
on q)/q. They don't give the same answer. How do you know which one to use?"
What would you say if you were Larry?
The only time you can use |E| = kq/r2 is when you want to find the magnitude of the electric field produced by the charge q.
You use (Fon q)/q to find the electric field at some location. You just put q into the field, measure the force on q, and divide to find E. q doesn't produce the electric field. You're using q to measure E.
Go to Contents
It depends on whether you want the field due to a charge.
Continue
Finding the electric field at a point Finding the electric field at a point
E=Fon q/q
Pick q.
Measure Fon q/q.
Calculate E.
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/page_05_layout.htm6/13/2005 8:44:36 PM page 5 of 16
You're going to be putting charges into electric fields so you can measure the field.
Do the sign and magnitude of the charge you use matter? How do you decide what charge to use?
If you use a positive charge to measure the electric field, E and Fon q will be in the same direction. You don't have to keep track of the negative sign on q.
You want to use a charge that doesn't affect the electric field you are trying to measure. What does that mean? Go to Contents positive charges are easier.
Submit
Finding the electric field at a point
E=Fon q/q
Pick q.
Measure Fon q/q.
Calculate E.
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/page_05a_layout.htm6/13/2005 8:44:54 PM page 5 of 16
For your measuring charge, q, not to affect an electric field, it has to have no effect on the charges that produce the electric field. You should be able to put q into the electric field without the charges that make the electric field moving.
metal rod with charges that produce an electric
field at the "x".
charges on rod move when q is put on the "x". This changes the
electric field at q's location.
Many textbooks call small, positive charges used to measure electric fields "test charges".
Go to Contents
Finding the electric field at a point Finding the electric field at a point
E=Fon q/q
q must not change E
source charges must not move
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/page_06_layout.htm6/13/2005 8:45:35 PM page 6 of 16
The gray disk is a piece of metal with some charges (the small green circles) on its surface. These charges produce an electric field that you want to measure. You have three charges available for measuring the electric field, q1, q2, and q3. Try each charge in the electric field and decide which one you should use to make the measurement.
Charge 1. Charge 2. Charge 3.
How did you make your choice? Go to Contents
It didn't move the green charges.
Finding the electric field at a point
E=Fon q/q
q must not change E
source charges must not move
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/page_08_layout.htm6/13/2005 8:46:50 PM page 7 of 16
You place an 8.0 x 10-15 C charge in an electric field and measure the force on it. You then remove the 8.0 x 10-15 C charge and place a 4.0 x 10-17 C charge at the same
location. You measure the force again and get a different number. You're sure the forces are right because you did this several times.
charge force on charge first try 8.0 x 10-15 C 1.5 x 10-12 N
second try 4.0 x 10-17 C 8.0 x 10-15 N
What value do you get for E using the 8.0 x 10-15 C charge? N/C
What value do you get for E using the 4.0 x 10-17 C charge? N/C
Go to Contents
188
200
Finding the electric field at a point Finding the electric field at a point
E=Fon q/q
q must not change E
source charges must not move
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/prob_01_layout.htm6/13/2005 8:47:46 PM page 9 of 16
Practice problem
The force on a +3 x 10-14 C charge placed in an electric field is
1.5 x 10-11 N to the left. The charges that create the electric
field do not move. What is the electric field at the location of the charge?
N/C
to the right to the left
Numbers in scientific notation should be written as 1e6 or 1e-6.
The electric field is 500 N/C to the left. The magnitude of the electric field is found by using
|E|=|Fon q|/|q|.
Substituting in numbers gives
|E|=(1.5 x 10-11 N)/(+3 x 10-14 C)=500 N/C.
The charge is positive, so the electric field is in the same direction as the force.
Go to Contents
500
Submit
Finding the electric field at a point
E=Fon q/q
q must not change E
source charges must not move
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/prob_02_layout.htm (1 of 2)6/13/2005 8:48:50 PM page 10 of 16
Practice problem
Joe is having trouble with this problem.
You use a charge q to measure an electric field. You then remove q and replace it with a charge q/2. Neither q nor q/2 disturb the source charges. What happens to the electric field?
The electric field doubles when q is replaced by q/2.
The electric field halves when q is replaced by q/2.
The electric field doesn't change when q is replaced by q/2.
He says "I don't know what it is. I know E=Fon q/q. If q gets smaller, Fon q gets smaller so E gets smaller. But, if q is in the denominator, and it gets smaller, E gets larger. It's the same equation, so why do I get two different answers?
How would you explain this problem to Joe?
Joe's right that Fon q/2 is smaller than Fon q. However, Joe is
forgetting that the force and the charge both change. The force is halved (Remember that Fon q/2 = (1/2)Fon q). The charge is
also halved. So
Go to Contents
If the source charges aren't disturbed E doesn't change.
Finding the electric field at a point
You get the same electric field whether you measure it with q or q/2.
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/prob_02_layout.htm (2 of 2)6/13/2005 8:48:50 PM
Finding the electric field at a point
E=Fon q/q q must not change E
source charges must not move
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/efo~13.htm6/14/2005 9:27:50 AM
page 11 of 16
There is an electric field in the rectangle below. The charges that create the electric field are not shown.
You can move q anywhere in the rectangle.
Which figure correctly shows the electric field vectors at A and B?
A B C
How can you tell which figure is correct?
Go to Contents
Finding the electric field at a point Finding the electric field at a point
E=Fon q/q
q must not change E
source charges must not move
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/efo~15.htm6/14/2005 9:31:47 AM page 12 of 16
Practice problem
What is the electric field at point A due to the green charges?
You can move q anywhere in the rectangle.
Click on the arrow that best represents the direction of the electric field at A.
magnitude: N/C
Go to Contents
|E| =
2.0 nC
|E| = 1.01 N/C.
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/prob_04_layout.htm (2 of 2)6/13/2005 8:51:37 PM
Finding the electric field at a point Finding the electric field at a point
E=Fon q/q
q must not change E
source charges must not move
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/prob_05_layout.htm6/13/2005 8:52:16 PM page 13 of 16
Practice problem
You use a charge q to measure the electric field at some location and get |E|=1500 N/C. You then use a charge 4q to repeat the measurement at the same location. What do you get for |E| the second time? Neither q nor 4q disturb the charges that produce the electric field.
N/C
Numbers in scientific notation should be written as 1e6 or 1e-6.
1500 N/C is correct.
The problem tells you that neither q nor 4q disturb the charges that make the electric field. This means that putting q or 4q into the electric field doesn't change the field.
Remember that the charge used to measure the electric field doesn't make the electric field, so |E|=k q/r2 isn't appropriate
for answering this question.
You can use E=Fon q/q to answer the question. You have to
remember that multiplying q by 4 also multiplies Fon q by 4, so
when you divide the 4's cancel.
Go to Contents
1500
Submit
Finding the electric field at a point
E=Fon q/q
q must not change E
source charges must not move
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/efo~17.htm6/14/2005 9:34:05 AM page 14 of 16
Practice problem
There is an electric field in the rectangular area below. What are its magnitude and direction at point A?
Click on the arrow that best represents the direction of the electric field at A.
magnitude: N/C
Describe how you found the electric field.
Go to Contents
Use 100 nC charge
Use 15 nC charge
Use 2 nC charge
Finding the electric field at a point
Do you get the same value of |E| if you use the 100 nC charge to measure it?
Finding the electric field at a point
E=Fon q/q
q must not change E
source charges must not move
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/efo~19.htm6/14/2005 9:39:53 AM page 15 of 16
There is a uniform electric field in the blue shaded area below. You fire a 0.04 gram positively charged particle into the field to measure it. Use the motion of the particle to find the electric field in the blue region.
Click on the arrow that best represents the direction of the electric field.
magnitude: N/C
Go to Contents
Fire particle
Stop
Finding the electric field at a point Finding the electric field at a point
E=Fon q/q
q must not change E
source charges must not move
file:///C|/My_dissertation/web_tutorial/Phase_IV/01_03_i/find_E/review_layout.htm6/13/2005 8:54:28 PM page 16 of 16
In this section you learned how to find the electric field at a location. You used the definition of the electric field,
E =
Fon q
q
To use this definition, remember that
q must not disturb the charges that create the electric field.
q is not the charge that creates the electric field.
You can find the electric field this way without knowing anything about the charges that make the electric field. You can close the browser to end this session or return to the Contents page and review another topic.
Go to Contents
