Magnetic Fields

Tanya Liu

Some Expectations

• Participate! Please don’t be scared, I would like to hear everyone’s voice

• Once again, if you don’t understand me, just raise your hand

• There will be some short assignments given• All my slides will be uploaded to Professor

Dodero’s site: http://my.liceti.it/prof/dodero/

Some Pronounciations

C1 = “C sub one” or “C one”

Some Pronounciations

• a + b = “a plus b”• a – b = “a minus b”• a x b = “a times b”• a/b = “a over b”• ab = “a to the b”• a2 = “a to the second/ a squared”• a3, a4 = “a to the third, a to the fourth, etc”• 0.05 = “zero point zero five”• 2x10-5 = “two times ten to the negative fifth”

Introduction to Magnetic FieldsWe know that charged objects produce electric fieldsWhat are sources of magnetic fields?

- permanent magnets- current

Introduction to Magnetic Fields: Permanent Magnets

A permanent magnet is made from magnetized material that consistently produces its own magnetic field– this is due to something known as ferromagnetism

Ferromagnetic materials can either form permanent magnets, or are attracted to magnets

Introduction to Magnetic Fields: Permanent Magnets

• A bar magnet is a permanent magnet, and consists of two poles, north and south

• The magnetic field lines leave from the north pole and enter the south pole

Introduction to Magnetic Fields: Permanent Magnets

• Opposite poles of a magnet attract each other, and like poles repel

Introduction to Magnetic Fields: Permanent Magnets

• when you break a magnet in half, you end up with two smaller magnets, both with north and south poles

• there are no magnetic monopoles

Introduction to Magnetic Fields: Permanent Magnets

• Magnetic Field of a Bar Magnet

How do we define a magnetic field?

• In electrostatics,

• Since magnetic monopoles don’t exist, however, this changes things a bit

eFE

q

How do we define a magnetic field?

• For a single charge q with velocity moving in a magnetic field there is a magnetic force on the charge:

sin

B

B

F qv B

F q vB

= perpendicular projection of onto

If ,

Cross Product Review

A B

A

B

A

B

sinA

sinA B A B

||A B

0A B

How do we define a magnetic field?

• the SI unit for is the tesla

Concept Question

If a moving charge traveling in the positive direction enters a magnetic field pointing in the positive direction, in which direction will the moving charge be deflected?a. - b. + c. - d. +

Concept Question Solution

Answer: b is correct. =

Magnetic force on a current-carrying wire

• we’ve seen that a single charge experiences a magnetic force,

• for a current-carrying wire of length l,

sin

B

B

F Il B

F IlB

Magnetic force on a current-carrying wire

is 0 when I=0, so the wire does not bend.

I is no longer 0, so now there is an , and the wire bends

The direction of current is reversed from B, so the wire bends in the opposite direction

A B C

Group Problem

A rectangular current loop with width a and length b is placed in a magnetic field, , as shown below. What is the net force felt by the loop, and what is the net torque?

Some Notes

• Homework assignment! Due on Friday, Jan 18th

A charged particle enters a magnetic field as shown below. What will the resulting path of the particle be?

a. circleb. straight linec. helix

Concept Question

𝑣

𝐵

Charged particle in a magnetic field

What happens to the path of a moving charged particle as it enters a magnetic field?

at all times, so the charge follows a circular path ( acts like centripetal force)

A charged particle enters a magnetic field as shown below. What will the resulting path of the particle be?

a. circleb. straight linec. helix

Concept Question

𝑣

𝐵

Charged particle in a magnetic field

If the particle has a component of velocity parallel to the magnetic field, it will follow a helical path

There is a component of parallel to at all times, so the charge still moves in a circle,it also moves in a path along the direction of

Group Problem

For a particle with charge q entering a magnetic field of magnitude with velocity at an angle of θ to the magnetic field, what is the radius of the circular path it travels, and what is the time it takes to complete one circle?

𝑣

𝐵

θ

Lorentz Force

• We know a charged particle in an electric field feels an electric force:

• We also know a moving charged particle in a magnetic field feels a magnetic force:

• The total force on a moving charged particle in an electric field and a magnetic field feels is the sum of these forces:

EF qE

BF qv B

( )E BF F F q E v B

An electron with charge –e and mass m is emitted from plate C and accelerated towards slit A. There is a potential difference between A and C, where .

a. What is the speed of the electron after it reaches A? (Use conservation of energy, electrical potential energy )

b. As the electron travels through the region after slit A, it passes through a downwards electric field , and a magnetic field into the page. At what velocity will the electron move in a straight line through this region?

c. Using your answers from part a and b, what is the charge to mass ratio of this electron (what is )?

Group Problem