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Department of Physics and Applied Physics95.144 Danylov Lecture 16
Lecture 16
Chapter 32
Magnetic ForceCyclotron motion
Course website:http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII
Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html
Physics II
Department of Physics and Applied Physics95.144 Danylov Lecture 16
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
Department of Physics and Applied Physics95.144 Danylov Lecture 16
Magnetic force on a moving charge
Department of Physics and Applied Physics95.144 Danylov Lecture 16
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.
Department of Physics and Applied Physics95.144 Danylov Lecture 16
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 qA) 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 qA) UpwardB) DownwardC) Into the screenD) Out of the screenE) The magnetic force is zero
The direction of the magnetic force on the proton is
Department of Physics and Applied Physics95.144 Danylov Lecture 16
Cyclotron MotionMany important applications of magnetism involve the motion of
charged particles in a perpendicular magnetic field
Department of Physics and Applied Physics95.144 Danylov Lecture 16
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.
Department of Physics and Applied Physics95.144 Danylov Lecture 16
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=0, which is a straight line
Note! The cyclotron frequency does not depend on v.
Department of Physics and Applied Physics95.144 Danylov Lecture 16
Cyclotron motion
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.
Department of Physics and Applied Physics95.144 Danylov Lecture 16
Aurora (Northern lights)
Charged particles(solar wind)
Department of Physics and Applied Physics95.144 Danylov Lecture 16
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)
, , ,
Department of Physics and Applied Physics95.144 Danylov Lecture 16
Cloud/Bubble chamber to detect charged particles
(contains a supersaturated vapor of water)
Department of Physics and Applied Physics95.144 Danylov Lecture 16
Magnetic force on Current-Carrying
Wires
Department of Physics and Applied Physics95.144 Danylov Lecture 16
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
Department of Physics and Applied Physics95.144 Danylov Lecture 16
There’s no force on a current-carrying wire parallel to a magnetic field.
Slide 32-139
Magnetic Forces on Current-Carrying Wires
∥
Department of Physics and Applied Physics95.144 Danylov Lecture 16
A current perpendicular to the field experiences a force in the direction of the right-hand rule.
Slide 32-140
Magnetic Forces on Current-Carrying Wires
Department of Physics and Applied Physics95.144 Danylov Lecture 16
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
Department of Physics and Applied Physics95.144 Danylov Lecture 16
Slide 32-147
Magnetic Forces Between Parallel Current-Carrying Wires: Current in Opposite Directions
Department of Physics and Applied Physics95.144 Danylov Lecture 16
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:
Department of Physics and Applied Physics95.144 Danylov Lecture 16
What you should readChapter 32 (Knight)
Sections 32.7 (Skip the Hall effect) 32.8 32.5 (skip)
Department of Physics and Applied Physics95.144 Danylov Lecture 16
Thank youSee you on Friday