1. Today4/11  Current Loops  “Phantom” magnets  Force/torque on loops in a B-field  B-Field due to many wires  HW: 4/11 “Torque on Loops” Due Wednesday, 4/16  Magnetism HW delayed till Monday 4/14 I will go over it today  Force on Loops and Torque on loops both due on Wednesday 4/16

2. Magnetic Torque, Loops What happens to loop? Turn the loop into a magnet. Magnets line up with the field. (A compass needle is a magnet!) Loop is a magnet (needle) centered in the loop with the N pole facing away from you. S The loop (magnet) will rotate so it lines up with the field. (S up and out of the page)

3. Magnetic Torque, Loops What happens to loop? S N The loop (magnet) will rotate so it lines up with the field. (S up and out of the page) Turn the loop into a magnet. Magnets line up with the field. (A compass needle is a magnet!) Loop is a magnet (needle) centered in the loop with the N pole facing away from you. This is a torque on the loop.

4. NS NS NS NS A bar magnet and current loop (powered by a battery) are shown in various orientations below. In each case the magnet if held in place and the current loop is released and allowed to rotate only about the axis shown. Determine if the loop will rotate. If so, find the direction of rotation and how far it rotates. If the loop is in unstable equilibrium, say so. (RHR #3) Torque clockwise from above, can’t turn North out Unstable equilibrium small tap will cause a 180° flip either direction. North right Clockwise (viewed from above) 90° North out Clockwise (viewed from above) 90° North in

5. Ampere’s Law E fieldB field E  1/r 2 point E  1/r rod of charge E  constant sheet of charge No point currents B  1/r wire “rod” of current B  constant sheet of current

6. Ampere’s Law B  1/r wire “rod” of current Sum of B times  l around any path =  0 times current through that path. I Sum(B x  l) = B x circ. = B2  r=  0 I B =  0 I/2  r (  1/r ) r Magnitude of the B-field given be this equation Direction by RHR #2 B Note: B always perpendicular to the radius

7. Magnetic Forces, Wires Find the force on wire 3 caused by wire 1 and 2. I2I2 I1I1 I3I3 r r 2 r

8. Magnetic Forces, Wires First find the direction of the B field at the X. All currents are the same I2I2 I1I1 B 1 =  0 I/2  r B 1&2 add as vectors B 2 = B 1 /  2 r Find B x,net and B y,net

9. Magnetic Forces, Wires Now find the force on wire 3. I2I2 I1I1 I3I3 F = I l B B 1&2