L15 Ch29 Magnetic Force - Faculty Server...

Department of Physics and Applied PhysicsPHYS.1440 Lecture15 A.Danylov

Lecture 15

Chapter 29

Magnetic ForceCyclotron motion

Course website:http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII

Physics II


Today we are going to discuss:

Chapter 29:

Section 29.7 (Skip the Hall effect) Section 29.8 Section 29.5 Skip


Electric Field Magnetic Field

From Coulomb’s law1

4̂

Biot-Savart law

4̂

Gauss’s Law

∙

Ampere’s Law

∙

So, now we know how to find magnetic fields using Bio-Savart and Ampere’s laws.Now, the question is “how does a magnetic field interact with material (which consists of charges and current)?”

Magnetic force on a moving charge

Magnetic force on current


Magnetic force on a moving charge


The Magnetic Force on a Moving ChargeAfter Oersted’s discovery, there were many other experiments with magnetic fields, currents, charges, etc. It was found that B exerts a force on a moving charge.

The magnetic force on a charge q as it moves through a magnetic field B with velocity v is:

where is the angle between v and B.


The Magnetic Force on a Moving Charge

A magnetic field has no effect on a charge moving parallel/antiparallel to the field

ConcepTest B field of q

A) To the rightB) To the left C) Into the screenD) Out of the screenE) The magnetic force is zero

The direction of the magnetic force on the proton is

ConcepTest B field of q

A) UpwardB) DownwardC) Into the screenD) Out of the screenE) The magnetic force is zero

The direction of the magnetic force on the proton is


Applications


Magnetic Force in “Art”

Nam June Paik’s Magnet TV (1965) at the truly amazing new Whitney Museum of American Art.

Magnet TV1965/99

Electrons in a kinescope are deflected by a

magnetic field

(a Korean‐American artist)Nam June Paik


Cyclotron Motion

Many important applications of magnetism involve the motion of charged particles in a perpendicular magnetic field

There is an amazingly beautiful application of


Cyclotron motionThe figure shows a positive charge moving in a plane that is

perpendicular to a uniform magnetic field.

B into page

Since F is always perpendicular to v, F changes the direction of the velocity, but not it is magnitude.It means q experiences only the centripetal accelerationThus, the charge undergoes uniform circular motion.

This motion is called the cyclotron motion of a charged particle in a magnetic field.


Cyclotron radius

B

Newton’s second law for a radial direction,

The frequency of the cyclotron motion.

The radius of the cyclotron orbit:

The period of the cyclotron motion:

If B=0, then rcyc=, which is a straight line

Note! The cyclotron frequency does not depend on v.


Cyclotron motion (general situation)

B

∥

The figure shows a more general situation in which the charged particle’s velocity is not exactly perpendicular to B.

The component of v parallel to Bis not affected by the field, so the charged particle spirals around the magnetic field lines in a helical trajectory.

The radius of the helix is determined by v, the component of v perpendicular to B.


Aurora (Northern lights)

Charged particles(solar wind)

Van Allen radiation belthttps://en.wikipedia.org/wiki/Van_Allen_radiation_belt


The Cyclotron

The first practical particle accelerator, invented in the 1930s, was the cyclotron.

Cyclotrons remain important for many applications of nuclear physics, such as the creation of radioisotopes for medicine.

The relevant equation for us is: .According to this equation, the bigger the charge, the smaller the radius.

ConcepTest Mass Spectrometer x x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xA B

Two particles of the same massenter a magnetic field with the same speed and follow the paths shown. Which particle has the bigger charge?

C) both charges are equalD) impossible to tell from the picture

Follow-up: What is the sign of the charges in the picture?

If q > 0, then the force is to the left (our case)

, , ,


Cloud/Bubble chamber to detect charged particles

(contains a supersaturated vapor of water)The photograph shows the track of anunusual positively charged particle with amass about equal that of an electron sloweddown by passing through a lead plate. Itwas among the earliest evidence of theexistence of the positron found by C.D.Anderson in 1932, but predicted by PaulDirac in 1928

lead plate

A gamma photon kicks out an electron out of an atom and creates an electron‐positron pair.


Magnetic force on Current-Carrying Wires


Magnetic Forces on Current-Carrying Wires We saw that a magnetic field exerts a force on a charge. A current consists of many moving charges, so a magnetic field should exert a force on a current.

The magnetic force on a segment dl:

The magnetic force of a charge:

If we apply this formula for a straight wire with a current I, then we will get:

Where l is a part of wire exposed to the magnetic field


There’s no force on a current-carrying wire parallel to a magnetic field.

Magnetic Forces on Current-Carrying Wires

∥

End of class


A current perpendicular to the field experiences a force in the direction of the right-hand rule.

Magnetic Forces on Current-Carrying Wires


Magnetic Forces Between Parallel Current-Carrying Wires: Current in Same Direction

We’ll treat I2 as a source of the magnetic field

Let’s find a force on current I1

Demo: Forces on a Current‐Carrying Wire


Slide 32-147

Magnetic Forces Between Parallel Current-Carrying Wires: Current in Opposite Directions


SummaryElectric Field Magnetic Field

Amperian loop

The magnetic force on a charge:

The magnetic force on a current:

From Coulomb’s law1

4̂

Bio-Savart law

4̂

Gauss’s Law

∙ ∙

The electric force on a charge:


Thank you

L15 Ch29 Magnetic Force - Faculty Server...

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