Today’s Concept: Torques in Magnetic Fields Physics 2112 Unit 13 Today’s Concept: Torques in Magnetic Fields Unit 13, Slide 1

Force on current carrying wire Last Time: y z x B F I This Time: Unit 13, Slide 2

Example 13.1 (Force on Wire) A wire is carrying 5amps through a magnetic field that is 50cm long and has a strength of 12 Gauss. What is the force on the wire? X X X X X X X I 0.5m Unit 13, Slide 3

Value of Torque |t| = 2*(W/2)*sin(Q)*(B*L) = W*L*B*sin(Q) = (Area of Loop)*B*sin(Q) z . B Q W final

Magnetic Dipole Moment Define: Area vector Magnitude = Area Direction uses R.H.R. Define: Magnetic Dipole moment Unit 13, Slide 5

m Makes Torque Easy! The torque always wants to line m up with B! m m turns m toward B x y z B m turns m toward B x y z “Dipole moments, I don't get how they are different from torques” Dipole moments tell you how much torque a given B field will place on a loop. |t| = |m||B|sinq Unit 13, Slide 6

Example 13.2 (Torque on Loops) 5A of current is moving clockwise through 20 loops of copper wire. The loops have a radius of 50cm and are placed in a 500 Gauss magnetic field as shown to the right. What is the torque on the loop? Unit 13, Slide 7

Magnetic Field can do Work on Current From Physics 2111: From Physics 2112: B m Define U = 0 at position of maximum torque Unit 13, Slide 8

CheckPoint 2A Three different orientations of a magnetic dipole moment in a constant magnetic field are shown below. Which orientation results in the largest magnetic torque on the dipole ? Biggest when Unit 13, Slide 9

CheckPoint 2B Which orientation has the most potential energy? Unit 13, Slide 10

CheckPoint 2C In order to rotate a horizontal magnetic dipole to the three positions shown, which one requires the most work done by the magnetic field? Unit 13, Slide 11

Example 13.3 (Rotating Loop) z z A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known. B . B 30˚ y y How much does the potential energy of the system change as the coil moves from its initial position to its final position. a I x final initial Conceptual Analysis A current loop may experience a torque in a constant magnetic field t = m X B We can associate a potential energy with the orientation of loop U = - m ∙ B The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. Strategic Analysis Find m Calculate the change in potential energy from initial to final Unit 13, Slide 12

Electric Dipoles Magnetic Dipoles Remember? Electric Dipoles Magnetic Dipoles + -

What’s all this good for? Many things. I’ll mention two….. one every day….. one high tech X . X . What if when it reaches this point, you reverse the direction of the current in the coil? Electric Motor

Magnetic Resonance Imaging (MRI) Protons have charge and spin…have magnetic moment Place in strong B field and m will try to align with field. m Will precess like top in gravity field (…remember from 2111?) Look for the signal from the precession and can spot protons in hydrogen Hydrogen is in water which is in soft tissue Magnetic Resonance Imaging (MRI)