Magnetic Force Cyclotron motion

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Cuthbert Giles Jefferson
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1 Lecture 15 Chapter 29 Physics II Magnetic Force Cyclotron motion Course website:

2 Today we are going to discuss: Chapter 29: Section 29.7 (Skip the Hall effect) Section 29.8 Section 29.5 Skip

3 Example Ampere s Law

4 Example The Magnetic Field of a Solenoid Take-home quiz Along the sides (bc, da), the line integral is zero since the field is perpendicular to the path. where n N/l is the number of turns per unit length. ds Along the bottom (ab), the B=0 line integral is zero since B 0 Amperian loop outside the solenoid. 0 abcda 0 0 abcda 0 There are N loops with current I enclosed by an Amperian loop, so B ds ds B / B Uniform field

5 Application of solenoids - MRI This patient is undergoing magnetic resonance imaging (MRI). The large cylinder surrounding the patient contains a solenoid that is wound with superconducting wire to generate a strong uniform magnetic field. B=1.2 T, I=100 A

6 The Magnetic Field Outside a Solenoid The magnetic field outside a solenoid looks like that of a bar magnet. Thus a solenoid is an electromagnet

7 Electric Field From Coulomb s law 1 4 Gauss s Law Magnetic Field Biot-Savart law 4 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

8 Magnetic force on a moving charge

The Magnetic Force on a Moving Charge After Oersted s

The magnetic force on a charge q as it moves through a

9 The Magnetic Force on a Moving Charge After 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.

10 The Magnetic Force on a Moving Charge A magnetic field has no effect on a charge moving parallel/antiparallel to the field

11 ConcepTest The direction of the magnetic force on the proton is B field of q A) To the right B) To the left C) Into the screen D) Out of the screen E) The magnetic force is zero

12 ConcepTest The direction of the magnetic force on the proton is B field of q A) Upward B) Downward C) Into the screen D) Out of the screen E) The magnetic force is zero

13 Applications

14 Magnetic Force in Art Electrons in a kinescope are deflected by a magnetic field Nam June Paik s Magnet TV (1965) at the truly amazing new Whitney Museum of American Art. Nam June Paik (a Korean American artist) Magnet TV 1965/99

15 There is an amazingly beautiful application of Cyclotron Motion Many important applications of magnetism involve the motion of charged particles in a perpendicular magnetic field

B into page Since F is always perpendicular to v, F changes the direction of the velocity, but not it is

16 Cyclotron motion The 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 acceleration Thus, the charge undergoes uniform circular motion. This motion is called the cyclotron motion of a charged particle in a magnetic field.

17 Cyclotron radius Newton s second law for a radial direction, B The radius of the cyclotron orbit: If B=0, then r cyc =, which is a straight line The period of the cyclotron motion: The frequency of the cyclotron motion. 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.

18 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 B is 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.

19 Thank you See you next time

Magnetic Force Cyclotron motion

Lecture 17 Chapter 29 Magnetic Force Cyclotron motion Messiah!? Miraculous appearance out of the blue. Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Today we are going to discuss: