1. -Magnetic Force on a Charged Particle -Magnetic Force on a Current-Carrying Wire -Torque on a Current-Carrying Loop
Fermi Lab, Chicago Illinois Circumference 6.3km
Mass Spectrometer
DC Motor
AP Physics C Mrs. Coyle

2. A magnetic field can exert a force on a charged particle that moves in it.

3. Three ways we talk about “magnetic field”.
Magnetic Field: Regions surrounding a magnet where another magnet or a moving electric charge will feel a force of attraction or repulsion.
Magnetic Field Lines: exit the north pole and enter the south.
Magnetic Field Strength, B
Vector, Unit: Tesla, T
Named after Nikola Tesla

4. Poles Law of Poles: Like poles repel, unlike poles attract.
The force between two poles varies as the inverse square of the distance between them.
A single pole (monopole) has not been isolated.

5. Force on a Charged Particle Moving in a Magnetic Field
-Magnetic fields only exert forces on moving charged particles or other magnets. 
F = |q|(v x B) = |q|vB sin q
vector cross-product
q is the angle between v and B
F=0 for q =0 or 1800

6. Remember: Cross Product Using Determinantsor

7. Remember: Properties of Cross Products of Unit Vectors
ixi=0 jxj=0 kxk=0
ixj=k jxk=i kxi=j

8. To find the direction of the force use the Right Hand Rule
For a positive test charge:
Thumb v
Fingers B
Out of palm F
The force is always perpendicular to the vB plane

9. For a negative particle the F is opposite to what it would be for a positive particle (use left hand)

10. Alternate Rule: Right Hand Curl Rule
Curl fingers from v to B
F = q(v x B)
F is in the direction of the thumb
Similarly used for the direction of torque (t=r x F)

11. Graphical Representation of the Magnetic Field Vector (Strength), B
x field lines pointing into the page ● field lines pointing out of the page

12. Question
Find the direction of the magnetic force acting on the +charged particle entering the magnetic field with a velocity v perpendicular to B.
x x x x x
V x x x x x
Answer: Upwards

13. What motion will the particle in the previous example undergo (particle entered the B-field in a direction perpendicular to B?
Circular Motion
Magnetic force will represent the centripetal force

14. Examples:

15. Does the magnetic force do work?
F is always perpendicular to the displacement
F can change the direction of v not the magnitude
F cannot do work, cannot change KE

16. Mass Spectrometer U.S. Department of Energy

17. Motion of Alpha- Beta-Gamma Particles in a Magnetic Field
1) Alpha particles, positive helium nuclei, charge +2e
2) Gamma rays, (no charge) electromagnetic radiation
3) Beta particles, electrons
charge -1e

18. Problem 1 A proton is accelerated through a constant electric field
(parallel plates) and acquires kinetic energy of 4eV.
It enters perpendicularly to the 2T field of a detector as shown.
Charge of a proton=1.6x10-19 C, mass of proton=1.67x10-27 kg, ignore gravity.
a) Draw the path of the positive charge as it enters the magnetic field.

19. Problem 1 cont’d
b) Calculate the force acting on the charge due to the magnetic field.
Charge of a proton=1.6x10-19 C , mass of proton=1.67x10-27 kg KE= 4eV B= 2T
Ans: v= 2.77x104 m/s, F= 8.86x10-15 N

20. Problem 1 cont’d
c) Calculate the distance on the detector where the particle will land (radius of the circular path). Ignore gravity.
Charge of a proton=1.6x10-19 C, mass of proton=1.67x10-27 kg KE= 4eV B= 2T
Ans: 1.45x10-4 m

21. Large Hadron Collider CERN (Conseil Européen pour la Recherche Nucléaire) Switzerland- France 2008 Circumference: 27km

22. Particle Accelerators use electric and magnetic fields to accelerate charged particles.
Cyclotron Applet

23. Magnetic Force on a Current Carrying Wire
F = I (L x B) = I L B sinq
I is the current
L is a vector of magnitude of the length of the wire and direction that of the current
q is the angle formed between I and B
What is the direction of the magnetic force acting on this wire? F

24. The force acting on a wire of arbitrary shape is the same as if it were a straight wire with the same ends
The total force is:

25. What is the net force acting on this current-carrying loop?

26. Which way will a loop turn?

27. Forces on a Current-Carrying Loop
For B as shown: F 1 = F3 = 0 F 2 = F4 = IaB Electric DC Motor (Fendt Applet)

28. F 2 = F4 = IaB Top View Torque Acting on the Current-Carrying Loop
Torque acting on the loop:

29. Torque Acting on the Current-Carrying Loop

30. Magnetic Force on a Current Carrying Wire
Lorentz Force- Magnetic Force on a Current Carrying Wire (Fendt Applet)

31. DC Motor

32. DC Motor

33. Problem #9
A proton moves with a velocity of v=(2i-4j+k)m/s in a region in which the magnetic field is B=(i+2j-3k)T. What is the magnitude of the magnetic force this charge experiences? Ans: 2.34x10-18 N

34. Problem #13
A wire 2.80 m in length carries a current of 5.00 A in a region where a uniform magnetic field has a magnitude of T. Calculate the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is (a) 60.0°, (b) 90.0°, (c) 120°.
Ans: a)4.73N, b)5.46N, c)4.73N

35. Problem # 21
A small bar magnet is suspended in a uniform T magnetic field. The maximum torque experienced by the bar magnet is 4.60 × 10–3 N · m. Calculate the magnetic moment of the bar magnet.
Ans: 18.4mA m2

36. Problem #54
A kg metal rod carrying a current of 10.0 A glides on two horizontal rails m apart. What vertical magnetic field is required to keep the rod moving at a constant speed if the coefficient of kinetic friction between the rod and rails is 0.100?
Ans: F=0.196N, B=0.039T