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

2. Lecture 14-2 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 E H develops  to both applied E and B.  Determines the sign and number of carriers.  Measures B. EHEH EHEH

3. Lecture 14-3 Carrier Sign and Density from Hall Effect Sign and density of charge carrier is determined at equilibrium and Hall voltage for a given current I and n EHEH EHEH

4. Lecture 14-4 Cyclotron "Dees" in constant magnetic field B Alternating voltage V is applied between the Dees at the orbital frequency f: "Magnetic Resonance Accelerator" Particle will acquire an additional kinetic energy  T = qV each time it crosses the gap (ie twice per revolution.. E=0 in Dees!). increases as v does problems  synchrotron

5. Lecture 14-5 Synchrotron R is the same since B increases as v does

6. Lecture 14-6 More complicated situations? helical motion (spiral) v is not perpendicular to B Van Allen belts Also non-uniform B magnetic bottle

7. Lecture 14-7 Polar Light High energy particles leaked out of the belt and interact with the earth atmosphere.

8. Lecture 14-8 Warm-up a)Increase E b)Increase B c)Turn B off d)Turn E off e)Nothing 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? http://canu.ucalgary.ca/map/content/force/elcrmagn/simulate/exb_thomson/applet.html http://canu.ucalgary.ca/map/content/force/elcrmagn/simulate/magnetic/applet.html

9. Lecture 14-9 Magnetic Force on a Current Loop –Force on top path cancels force on bottom path (F = IBL) –Force on right path cancels force on left path. (F = IBL) Force on closed loop current in uniform B? Uniform B exerts no net force on closed current loop. closed loop

10. Lecture 14-10 Magnetic Torque on a Current Loop If B field is  to plane of loop, the net torque on loop is also 0. Definition of torque: abut a chosen point If B is not , there is net torque. B

11. Lecture 14-11 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.

12. Lecture 14-12 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: dI

13. Lecture 14-13 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.  Therefore,  B x .

14. Lecture 14-14 Potential Energy of Dipole Illustrated B x  B x  B x   = 0 U = -  B  = 0 U =  B negative work  =  B X U = 0 positive work (by YOU) min. energymax. energy max torque

15. Lecture 14-15 PHYS241 - 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

16. Lecture 14-16 PHYS241 - 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

17. Lecture 14-17 PHYS241 - 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