Wed. Feb. 11 – Physics Lecture #29 Magnetic Forces 1. Magnetic Forces on Charged Particles 2. Motion in Magnetic Fields 3. Magnetic Forces on Current-Carrying Conductors Warm-Up, Discuss with Neighbors: A uniform magnetic field in this room points from the floor towards the ceiling. What is the direction of the magnetic force acting on the particles in the various situations below? a) A motionless proton? b) A proton moving towards the front of the room? c) An electron moving towards the front of the room? d) A neutron moving towards the front of the room? e) A proton moving straight up toward the ceiling? f) An electron moving to the right? g) A proton moving diagonally from the back right to the front left?

Example: Calculate the magnetic force acting on a particle with charge q moving with velocity in a magnetic field Example: A particle with charge q moves with speed v at an angle of 30 degrees North of East. It enters a region of space with uniform magnetic field B directed at an angle of 10 degrees West of North. Determine the magnetic force (magnitude and direction) acting on the particle when it enters the magnetic field.

ConceptCheck: An electron and a proton move with the same velocity. They enter a region that has a uniform magnetic field directed into the page as shown. Which of the following sketches best represents their paths? Neglect their interactions with each other. x x x x x x x p e p e

ConceptCheck: A charged particle is in a region of space with a uniform magnetic field (no other fields are present). Which of the following describes a possible path the charged particle can travel? (Put up as many cards as you think possible.) 1. No motion 2. Straight line 3. Parabola 4. Circle 5. Helix 6. Square

Magnetic Forces and Circular Motion: How do we determine the radius of any circular motion associated with magnetic forces? Magnetic Forces & Work: A charged particle is in a region of space with a uniform magnetic field (no other fields are present). What can we say about the change in kinetic energy of the charged particle?

Example: Velocity Selector An electron travels with velocity through a region of uniform magnetic field directed out of the page as shown. The electron is moving in a straight line. How do you know there must be another field present? If the other field is a uniform electric field, what is its direction? What is the magnitude of this electric field? What happens if you send in a particle with charge +2e but the same velocity? What happens if you send in an electron with a slower speed (but same direction?) x x x x x x x

Example: Wire in Field. A conducting wire is in a uniform magnetic field directed up as shown. Conventional current I flows in the wire towards the left. a) What is the direction of the magnetic force? b) What is the magnitude of this magnetic force? c) What if the wire were angled at 30 degrees with respect to horizontal? d) Return to the original scenario. The actual charge carriers in this wire are electrons, so the electron current flows in the wire towards the right. What is the direction of the magnetic force? e) We argued previously that magnetic forces do no work. How can the wire start from rest and begin to move?

Example: Hall Effect. A wire is held fixed in a uniform magnetic field pointing into the page. The wire carries current I going towards the right. ConceptCheck: If the charge carriers were positively charged, what would be the sign of  V bottom  top = V top – V bottom, the potential difference between the top side and the bottom side of the wire? 1.  V > 0 2.  V = 0 3.  V < 0 4. Not enough info What would be different if the charge carriers were negative instead of positive? What is the potential difference between the top and bottom side of the wire? Assume known distances. x x x x x x x top bottom I