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:  Gravitational  Electrostatic  Magnetic 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 < F J < H < I

Test Charge – Electric Field Intensity Formula q is the charge of the source q t is the charge of the test charge Divide your electrostatic force formula by the test charge E = Fe/qt This is the electric field intensity

Where … E = electric field intensity (N/C) F Q = F e = electric force (N) q t = Electric charge (C) of test charge

Field Intensity at a Point Example 1: A positive charge of 3.2 x 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, q t = x C, is placed in an electric field and experiences a force of F = 4.0 x 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 C if it replaced the test charge.

Answer

Practice Problems Page 646  Questions 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 GravitationalElectrostaticMagnetic AttractiveAttractive or repulsive Inverse square behaviour Depends on mass Depends on charge Depends on pole strength

Comparing Forces GravitationalElectrostaticMagnetic 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 mass Magnetic 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

Practice Problems Page 649  Questions 15-18, 19*** (challenge – remember centripetal acceleration!)