Oregon State University PH 213, Class #21 These slides can serve as a follow-up summary for a video-recorded presentation, which you can access here. 5/19/17 Oregon State University PH 213, Class #21

The Source of the Magnetic Field: Moving Charges The magnetic field of a charged particle q moving with velocity v is given by the Biot-Savart law: where r is the distance from the charge and θ is the angle between v and r. The Biot-Savart law can be written in terms of the cross product as 5/19/17 Oregon State University PH 213, Class #21

Oregon State University PH 213, Class #21 Applications 5/19/17 Oregon State University PH 213, Class #21

Magnetic Field of a Current in a Straight Wire At any point in space, the field magnitude B caused by a current I flowing in a long straight wire, is proportional to I and inversely proportional to the radial distance r from the point to the wire: B = 0I/(2r) The proportionality here, 0/2, uses the definition of the coulomb (since I = q/t), and it also reflects the geometry and properties of space itself (much as k does for electric fields: E = kq/r2). 0 = 4 x 10-7 T·m/A What is the direction of the field due to current in a straight wire? Use Right-Hand Rule # 2: Point your right-hand thumb along the (positive) current direction. Your fingers will then curl around the wire in the direction of the B-field that current is causing. As with all magnetic fields, these lines are closed loops. 5/19/17 Oregon State University PH 213, Class #21

Right-hand rule #2: For fields 5/19/17 Oregon State University PH 213, Class #21

Oregon State University PH 213, Class #21 5/19/17 Oregon State University PH 213, Class #21

Oregon State University PH 213, Class #21 Here again is the field strength due to current in a straight wire: B = 0I/(2r) A good summary problem: On a 3-D set of coordinate axes: If a wire along the y-axis carries a current in the positive y-direction, which of these identical charges q, each moving with the same speed v, will experience the greatest magnetic force magnitude? 1. q at (2,0,0), moving parallel to the x-axis. 2. q at (3,0,0), moving parallel to the x-axis. 3. q at (3,0,0), moving parallel to the y-axis. 4. q at (2,0,0), moving parallel to the z-axis. 5. q at (1,0,0), moving parallel to the z-axis. 5/19/17 Oregon State University PH 213, Class #21