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

Magnetic Torque, LoopsWhat 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)

Magnetic Torque, LoopsWhat 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.

N S

N S

N S

N S

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 turnNorth 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

Ampere’s LawE field B field

E 1/r2 point

E 1/r rod of charge

E constantsheet of charge

No point currents

B 1/r wire“rod” of current

B constantsheet of current

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. = B2r = 0I

B = 0I/2r ( 1/r )r

Magnitude of the B-field given be this equationDirection by RHR #2

B

Note: B always perpendicular to the radius

Magnetic Forces, WiresFind the force on wire 3 caused by wire 1 and 2.

I2 I1

I3

r

r2 r

Magnetic Forces, WiresFirst find the direction of the B field at the X. All currents are the same

I2 I1

B1 = 0 I/2 r

B1&2 add as vectors

B2 = B1/ 2

r

Find Bx,net and By,net

Magnetic Forces, WiresNow find the force on wire 3.

I2 I1

I3

F = I l B

B1&2