Announcements WebAssign HW Set 6 due this Friday Problems cover material from Chapters 19

1. Announcements • WebAssign HW Set 6 due this Friday • Problems cover material from Chapters 19 • Prof. Kumar tea and cookies today from 5 – 6 pm in room 2165 • mine are 2 - 3 pm Thursday, room 2265 • also, can schedule by appointment • Exam 1 statistics • QUESTIONS? PLEASE ASK!

2. Average: 14.43 • Standard deviation: 3.44

3. From last time • Magnets and earth’s magnetic field • Magnetic Fields: • Units are T = N/A.m • Use right hand rule to determine direction of force • Force on a wire: F = B I L sin θ

4. Torque on a Current Loop • Torque t = B I A N sin q • Applies to any shape loop • N is the number of turns in the coil • Torque has a maximum value of NBIA (when q = 90°) • Torque is zero when the field is parallel to the plane of the loop • Magnetic Moment m = IAN • mis a vector • Torque can be written as t = mB sinq m

5. Example Problem 19.31 • A long piece of wire with a mass of 0.100 kg and a length of 4.00 m is used to make a square coil with a side of 0.100 m. The coil is hinged along a horizontal side, carrying a 3.40 A current, and is placed in a vertical magnetic field of 0.010 T. (a) Determine the angle that plane of the coil makes with the vertical when the coil is in equilibrium. (b) Find the torque acting on the coil due to the magnetic force at equilibrium

6. Electric Motor • electric motor - converts electrical energy to mechanical energy • The mechanical energy is in the form of rotational kinetic energy • An electric motor consists of a rigid current-carrying loop that rotates when placed in a magnetic field

7. Electric Motor • Torque acting on the loop will rotate the loop to smaller values of θ until the torque becomes 0 at θ = 0° • If the loop turns past this point and the current remains in the same direction, the torque reverses and turns the loop in the opposite direction • Bad!!

8. Electric Motor • So, we need to be clever… • To provide continuous rotation in one direction, the current in the loop must periodically reverse • In AC motors, this reversal naturally occurs • In DC motors, a split-ring commutator and brushes are used • Actual motors would contain many current loops and commutators

9. Force on a Charged Particle in a Magnetic Field • Consider a particle moving in an external magnetic field so that its velocity is perpendicular to the field • The force is always directed toward the center of the circular path • The magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle

10. Force on a Charged Particle • Equating the magnetic and centripetal forces: • Solving for r: • r is proportional to the momentum of the particle and inversely proportional to the magnetic field • Sometimes called the cyclotron equation

11. Particle Moving in an External Magnetic Field • If the particle’s velocity is not perpendicular to the field, the path followed by the particle is a spiral • The spiral path is called a helix

12. Example Problem 19.42 • A cosmic ray proton in interstellar space has an energy of 10 MeV and executes a circular orbit having a radius equal to that of Mercury’s orbit around the Sun (5.8 x 1010 m). What is the magnetic field in that region of space?

13. Solution to 19.31

14. Solution to 19.42