Unit3 Worksheet v7 - Physics

Unit 3: Electric Fields

I. Analogy to electric field: Wind1

The point of this tutorial is to introduce electric fields.

But instead of doing so immediately, we'll start with an analogy to wind. A. An industrial--strength fan creates the wind pattern indicated in this

diagram.

Someone holds a small kite at point A.

Then the person holds a larger kite at that same point.

In both cases, the kite directly faces the fan and therefore catches the wind. 1. In what sense is the wind stronger on the large kite than it is on

the small kite?

2. In what sense is the wind equally strong at both kites?

3. A student says,

The wind itself is equally strong at point A no matter which kite you hold there--or even if you don't hold a kite there.

The large kite feels more force than the small kite because it has more area and therefore catches more wind, not because the wind itself is stronger. Does this student agree with the answers you just gave?

If not, do you think the student makes good points?

In what ways do you disagree?

1Section I adapted from Open Source Tutorials in Physics Sensemaking, Suite 2 ? University of Maryland Physics Education Research Group, 2010

Unit 3 Worksheet-- 1

As a convenient catchphrase, let's define the wind field as the strength and direction of the wind itself at a given point (whether or not an object is held there).

So, according to the student, the wind field at point A stays the same whichever kite you put there; but that same wind field produces a different wind force on kites of different sizes.

Now you'll figure out a way to define the wind field more precisely. 4. The smaller kite has cross--sectional area 0.50 m2.

When held at point A, it feels a wind force of

3.0 N.

The larger kite has exactly twice the cross--sectional area (1.0 m2) of the smaller kite.

What wind force would you expect the larger kite to feel at point A?

Explain.

5. Now a kite of cross--sectional area 2.0 m2 is held at point A.

What wind force do you expect it to feel?

Why?

6. Here's the punch line.

Each of the three kites from question (4) and (5) feels a different wind force at point A.

But they should each feel the same wind field because the wind itself is the same at point A no matter which kite you hold there.

Is there some number having to do with wind force and cross--sectional area that's the same for all three kites and could therefore work as a definition of wind field?

This is hard; try it for a while, and if you get stuck, move on to the next question.

7. Here are two proposed definitions of wind field:

(i) wind field = wind force ? cross--sectional area, or (ii) wind field = wind force ? cross--sectional area.

Which of those definitions, if either, better captures the intuitive sense of what wind field is supposed to mean?

8. Let's think more about the "better" definition of wind field from question (7).

What are the units of that number?

Unit 3 Worksheet-- 2

9. Explain what that definition of wind field means in terms your roommate could understand

(assuming your roommate isn't a physics person).

Consult an instructor before you proceed.

B. Does the wind force depend on the fan, the kite, or both?

What about the wind field?

Briefly explain.

II. Applying field ideas to electric stuff2

We just saw that the wind field is the strength and direction of the wind, independent of whether the wind acts on anything.

In general, a field is the strength and direction of something, independent of whether that something acts on an object.

Let's apply these ideas to electric fields.

A glass rod is given a positive charge by rubbing it with silk. Below is a side and top view of the rod, with a few test points labeled.

A. Sketch vectors at each of the

Rod

A

B

points marked with a

to

represent the electric force

exerted on a positive test charge

if it were at that location.

Rod A B

Side View

Top View

How does the magnitude of the

force exerted on the test charge at point A compare to the magnitude of the force on the test charge at

point B?

2Section II adapted from Open Source Tutorials in Physics Sensemaking, Suite 2 ? University of Maryland Physics Education Research Group, 2010. & McDermott, L. C. et al. Tutorials in Introductory Physics. Prentice Hall, 2002. & Dr. Beth Thacker PHYS 1404 Unit 03 Lab: Electric Field

Unit 3 Worksheet-- 3

B. Suppose the value of the charge, qtest, on the test charge were halved.

Would the electric force exerted on the test charge at each location change? If so, how? If not, explain why not.

Would the ratio /!"#! change at each location? If so, how? If not, explain why not.

C. The quantity /!"#! evaluated at any point is called the electric field

at that point.

How does the magnitude of the electric field at point A compare to the magnitude of the electric field at point B? Explain.

D.

Sketch vectors at each of the points marked with a

to represent the electric field

at that location.

Would the magnitude or the direction of the electric field at point A change if:

? the

charge on the rod were increased? Explain.

Rod A B

Top View

? the magnitude of the test charge were increased? Explain.

? the sign of the test charge were changed? Explain

Unit 3 Worksheet-- 4

You have been representing the electric field due to a configuration of electric charges by an arrow that indicates magnitude and direction of the field at a particular point. This is the conventional or vector representation of an electric field.

An alternative representation of the vector field involves defining electric field lines.

E. At right is a series of diagrams with electric field lines drawn for +1C, +2C, and --1C charges.

a. From looking at the diagrams how do you tell where the field is strongest? Explain.

How do you tell where the field is weakest? How do you tell the direction of the field? Explain.

b. Based on the diagrams for electric field lines, draw a diagram at right with electric

field lines for +3C charge.

c. Draw an electric field line diagram for ?1.5C charge.

d.

Is there an electric field at points in space where there are no electric field lines drawn?

Explain

Consult an instructor before you proceed.

III. From concepts to problem solving3

To correctly apply the formula for the electric field, you need to relate it to the underlying concepts when thinking through a problem. This problem gives you practice doing so when you have lots of information to deal with.

If you find yourself getting confused, think back to the wind.

3Section IV adapted from Open Source Tutorials in Physics Sensemaking, Suite 2 ? University of Maryland Physics Education Research Group, 2010

Unit 3 Worksheet-- 5

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