Lecture 14 1 Magnetic Field B Magnetic force

Lecture 14 -1 Magnetic Field B • Magnetic force acting on a moving charge q depends on q, v. A (q>0) If q<0

Lecture 14 -2 Both B and E present when balanced velocity selector No deflection when E=3 k. V/m, B=1. 4 G http: //canu. ucalgary. ca/map/content/force/elcrmagn/simulate/exb_thomson/applet. html

Lecture 14 -3 Hall Effect • A conducting strip in crossed E and B fields • Applied E along the strip leads to a charge buildup on the sides of the strip and thus an electric field EH develops to both applied E and B. EH Ø Determines the sign and number of carriers. EH Ø Measures B.

Lecture 14 -4 Carrier Sign and Density from Hall Effect Sign and density of charge carrier is determined at equilibrium Hall voltage EH and EH for a given current I and n

Lecture 14 -5 Cyclotron • "Magnetic Resonance Accelerator" • "Dees" in constant magnetic field B • Alternating voltage V is applied between the Dees at the orbital frequency f: • Particle will acquire an additional kinetic energy T = q. V each time it crosses the gap (ie twice per revolution. . E=0 in Dees!). increases as v does problems synchrotron http: //www. kgv. net/amorrison/assets/animations/cyclotron. swf

Lecture 14 -6 Synchrotron R is the same since B increases as v does

Lecture 14 -7 More complicated situations? v is not perpendicular to B Also non-uniform B magnetic bottle helical motion (spiral) Van Allen belts

Lecture 14 -8 Polar Light High energy particles leaked out of the belt and interact with the earth atmosphere.

Lecture 14 -9 Warm-up An electron (charge -e) comes horizontally into a region of perpendicularly crossed, uniform E and B fields as shown. In this region, it deflects upward as shown. What can you do to change the path so it remains horizontal through the region? a) b) c) d) e) Increase E Increase B Turn B off Turn E off Nothing http: //canu. ucalgary. ca/map/content/force/elcrmagn/simulate/magnetic/applet. html http: //canu. ucalgary. ca/map/content/force/elcrmagn/simulate/exb_thomson/applet. html

Lecture 14 -10 Magnetic Force on a Current Loop Force on closed loop current in uniform B? – Force on top path cancels force on bottom path (F = IBL) – Force on right path cancels force on left path. (F = IBL) closed loop Uniform B exerts no net force on closed current loop.

Lecture 14 -11 Magnetic Torque on a Current Loop Definition of torque: abut a chosen point • If B field is to plane of loop, the net torque on loop is also 0. B • If B is not , there is net torque.

Lecture 14 -12 Calculation of Torque • Suppose the coil has width b (the side we see) and length a (into the screen). The torque about the center is given by: area of loop • Define magnetic dipole moment by where n is normal to the loop with RHR along I.

Lecture 14 -13 Example of Magnetic Moment Calculation A thin non-conducting disk of mass m and uniform surface charge density rotates with angular velocity as shown. What is the magnetic moment? mag. moment of the ring shown: d. I

Lecture 14 -14 Potential Energy of Dipole • Work must be done to change the orientation of a dipole (current loop) in the presence of a magnetic field. • Define a potential energy U (with zero at position of max torque) corresponding to this work. q Þ Therefore, Þ B x Þ .

Lecture 14 -15 Potential Energy of Dipole Illustrated m B m x B B m x x t=0 t = m. B X t=0 U = -m. B U=0 U = m. B min. energy max torque negative work max. energy positive work (by YOU)

Lecture 14 -16 PHYS 241 - Quiz A An electron (charge e) comes horizontally into a region of perpendicularly crossed, uniform E and B fields as shown. In this region, it is deflected upward as shown. What can you do to change the path so it deflects downward instead through the region? a. Increase E b. Turn B off c. Decrease E d. Slow down the electron e. None of the above

Lecture 14 -17 PHYS 241 - Quiz B A proton (charge +e) comes horizontally into a region of perpendicularly crossed, uniform E and B fields as shown. In this region, it goes straight without deflection. What can you do to change the path so it deflects upward through the region? a. Increase E b. Increase B c. Turn B off d. Slow down the proton e. None of the above

Lecture 14 -18 PHYS 241 - Quiz C A proton (charge +e) comes horizontally into a region of perpendicularly crossed, uniform E and B fields as shown. In this region, it deflects downward as shown. What can you do to change the path so it remains horizontal through the region? a. Increase E b. Turn B off c. Turn E off d. Slow down the electron e. Increase B