Field Theory

Physics 12

Field Theory

When forces exist without contact, it can be useful to use field theory to describe the force experienced by a particle at any point in space

We have previously considered gravitational fields and seen that gravitational fields are the result of mass creating the field and the distance an object is placed from the mass

Draw a diagram of what you think a gravitational field would look like.

Fields

There are three common forces that act without contact between objects:GravitationalElectrostaticMagnetic

Since these forces do not require contact, field theory is often used to describe the force that results on an object within the field (ie, not touching)

How do we know what a field looks like then???

Electric Field Mapping

To map an electric field, a small test charge is placed in the field and the magnitude and direction of the force is recorded

The test charge is then moved throughout the electric field and a map of the field is created

The force experienced by the test charge will be the result of Coulomb’s Law

Test charge is a positive charge

Imagine a positively charged particle…

Electric Field Mapping

If a positive charge was put in this field, it would repel (outward arrows).

As you get farther from

the charged particle, the

repulsion gets less and

less.

The arrows represent the

FORCE.

What would a negatively charged particle’s field look like?

Test Charge

The test charge that is used must be small compared to the charge creating the field

If not, the test charge’s field will change the field that is being investigated

The electric field should be the same regardless of the test charge used

Multiple charges in a field

What would a field look like for one positively and one negatively charged particle?

Field Lines – Two Opposing Charges

How do I know the arrow points to the – not +?

Positively charged particles create outward arrows and vice versa

What do you think…

Will happen when two positive charges of equal strength are put together? What will the field look like?

Field Lines – Two Positive Charges

What do you think…

Will happen when two positive charges are put together? What will the field look like?

Problem

What are the relative magnitudes of the charges in the diagram?

What is the polarity of each of the charges?

*** NOTES

More dense field lines means greater charge

Electric field lines never cross each other

Multiple Charges

It is also possible to consider what happens with multiple charges:

Check Your Understanding

1.Several electric field line patterns are shown in the diagrams below. Which of these patterns are incorrect? Why?

C, D, E

Check Your Understanding

2. What is wrong with this diagram?

d

DAECB

Objects A, C, F, G, H and I are positive.

B < A C < D

G < E < FJ < H < I

Test Charge – Electric Field Intensity Formula

q is the charge of the sourceqt is the charge of the test

charge

Divide your electrostatic force formula by the test charge

E = Fe/qtThis is the electric field

intensity t

e

t

e

t

t

t

e

te

q

FE

r

kq

q

F

rq

kqq

q

Fr

kqqF

2

2

2

Where …

E = electric field intensity (N/C)FQ = Fe = electric force (N)

qt = Electric charge (C) of test charge

Field Intensity at a Point

Example 1: A positive charge of 3.2 x 10 -5 C experiences a force of 4.8N right when placed in an electric field. Find the magnitude and direction of the field, at that location.

Draw a picture of what this might look like.

Example 2

A positive test charge, qt = + 2.0 x 10-9 C, is placed in an electric field and experiences a force of F = 4.0 x 10-9 N [W].

A) What is the electric field intensity at the location of the test charge?

B) Predict the force that would be experienced by a charge of +9.0 x 10-6 C if it replaced the test charge.

Answer

Practice Problems

Page 646Questions 12-14

So what do you think would happen…

If we wanted a diagram of Earth and Moon (gravitational charge instead of electrostatic)?

What do you think…

A field would look like around a “regular” magnet (one North and one South pole)?

Comparing Forces

Gravitational Electrostatic Magnetic

Attractive Attractive or repulsive

Attractive or repulsive

Inverse square behaviour

Inverse square behaviour

Inverse square behaviour

Depends on mass

Depends on charge

Depends on pole strength

Comparing ForcesGravitational Electrostatic Magnetic

Weaker than other two

Lines go toward mass

lines run out of a positive

charge and into a negative

charge

lines are actually closed loops running out of a north pole and into a south pole

Field Lines Summary

Graphical representation of the field surrounding a point charge/mass or series of charges/poles

Electric fields: lines run out of a positive charge and into a negative charge

Gravitational fields: lines all go toward a massMagnetic field lines: lines are actually closed

loops running out of a north pole and into a south pole

Gravitational Field

The strength of a gravitational field can be determined using a test mass

Like with a test charge, the test mass should be small

In a manner similar to the electric field, we will divide out the test mass

t

g

t

g

t

t

t

g

tg

m

Fg

r

Gm

m

F

rm

Gmm

m

Fr

GmmF

2

2

2

Practice Problems

Page 649Questions 15-18, 19*** (challenge – remember

centripetal acceleration!)