Magnetic Force Cyclotron motion

Transcription

1 Lecture 17 Chapter 29 Magnetic Force Cyclotron motion Messiah!? Miraculous appearance out of the blue. 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 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

4 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

5 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

6 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

7 Magnetic force on a moving charge

8 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.

9 Let s play with the Magnetic Force on a Moving Charge A magnetic field has no effect on a charge moving parallel/antiparallel to the field

10 Applications

11 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

12 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

13 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.

14 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.

15 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.

16 Aurora (Northern lights) Charged particles (solar wind) Van Allen radiation belt

17 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.

18 (contains a supersaturated vapor of water) Cloud/Bubble chamber to detect charged particles lead plate The photograph shows the track of an unusual positively charged particle with a mass about equal that of an electron slowed down by passing through a lead plate. It was among the earliest evidence of the existence of the positron found by C.D. Anderson in 1932, but predicted by Paul Dirac in 1928 A gamma photon kicks out an electron out of an atom and creates an electron positron pair.

19 Magnetic force on Current- Carrying Wires

20 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 of a charge: The magnetic force on a segment dl: 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

21 Magnetic Forces on Current-Carrying Wires There s no force on a currentcarrying wire parallel to a magnetic field. End of class

22 Magnetic Forces on Current-Carrying Wires A current perpendicular to the field experiences a force in the direction of the right-hand rule.

23 Magnetic Forces Between Parallel Current- Carrying Wires: Current in Same Direction Let s find a force on current I 1 We ll treat I 2 as a source of the magnetic field Demo: Forces on a Current Carrying Wire

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

25 Summary Electric Field Magnetic Field From Coulomb s law 1 4 Gauss s Law The electric force on a charge: Bio-Savart law 4 Amperian loop The magnetic force on a charge: The magnetic force on a current:

26 Thank you