Example: Magnetic Force Directions from Right Hand Rule 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? Example: Magnetic Force & Vectors Calculate the magnetic force acting on a particle with charge q moving with velocity in a magnetic field a) A motionless proton? b) A proton moving towards the front of the room? An electron moving towards the front of the room? A neutron moving towards the front of the room? d) A proton moving straight up toward the ceiling? e) An electron moving to the right? f) A proton moving diagonally from the back right to the front left?
ConcepTest #11: 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? x x x x x x x p e
ConcepTest #12: 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.) Discussion: 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? No motion 4. Circle Straight line 5. Helix Parabola 6. Square B-field Paths
x x x x x x x Example: Velocity Selector An electron travels with velocity through a region of uniform magnetic field directed into 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? x x x x x x x
x x x x x x x Example: Velocity Selector An electron travels with constant velocity through a region of uniform magnetic field directed into the page (as shown) and uniform electric field pointing down (not shown). 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: Current-carrying wire in Magnetic Field A conducting wire is in a uniform magnetic field directed to the left as shown. a) Conventional current I flows in the wire towards the top of the page. Conventional current is the motion of positive charges. What is the direction of the magnetic force? b) The actual charge carriers in this wire are electrons, so the electron current is towards the bottom of the page. What is the direction of the magnetic force? Think about This: if magnetic forces do no work, how can the wire start from rest and begin to move?
x x x x x x x I Example: Hall Effect A wire is held fixed in a uniform magnetic field pointing into the page as shown. The wire carries conventional current I going towards the right. x x x x x x x top bottom I If the charge carriers were positively charged, what would be the sign of DVbottomtop = Vtop – Vbottom, the potential difference between the top side and the bottom side of the wire? What is the potential difference between the top and bottom side of the wire? Assume you know/can measure the distance (thickness) of the wire. Think about This: Would anything be different if the charge carriers were negative instead of positive?
(back of card) No direction (zero) ConcepTest #13: A square loop of wire with sides of length L carries a current I in a clock-wise direction; the current loop is in a uniform magnetic field B that is in the plane of the page and pointing to the right, as shown. Consider the following choices: 1. Up 4. Left 2. Down 5. Into the page 3. Right 6. Out of the page (back of card) No direction (zero) c) What is the direction of the net torque acting on the entire loop? (Take center of loop as reference point.) a) What is the direction of the magnetic force acting on the right hand piece of the loop? b) What is the direction of the net magnetic force acting on the entire loop? Think about This: assuming the loop started from rest, what would be its subsequent motion?
Current Loops, Magnetic Moments, and Torque A current loop can be treated using a magnetic moment model. In this model, replace the current loop with a little bar magnet (the magnetic moment). N S Consider a uniform magnetic field pointing to the right as shown. A little bar magnet is placed in the field; the magnet is free to pivot (in three dimensions) about its center. What is the direction of the torque acting on this magnetic moment? N = number of turns of wire in loop A = area of loop I = current in loop Direction from RHR II: curl fingers in direction of current, thumb points in direction of magnetic moment.
(back of card) No direction Example: Torque on Current Loop The plane of a current loop (N = 10, A = 0.01 m2 , I = 1 A,) makes an angle of 30o with a uniform magnetic field of magnitude 0.2 T directed to the right, as shown in the figure. Assume the current is going into the page at the lower left hand part of the loop and out of the page at the upper right hand part of the loop, as indicated on the sketch 30o What is the magnitude of the torque acting on the loop? ConcepTest #14: What is the direction of the torque acting on this current loop? Hold up as many cards as you need to specify the direction. 1. Up 4. Left 2. Down 5. Into the page 3. Right 6. Out of the page (back of card) No direction