Magnetic Forces

1. Magnetic Forces

2. Forces in Magnetism • The existence of magnetic fields is known because of their affects on moving charges. • What is magnetic force (FB)? • How does it differ from electric force (FE)? • What is known about the forces acting on charged bodies in motion through a magnetic field? • Magnitude of the force is proportional to the component of the charge’s velocity that is perpendicular to the magnetic field. • Direction of the force is perpendicular to the component of the charge’s velocity perpendicular to the magnetic field(B).

3. Magnetic Force (Lorentz Force) FB = |q|vB sinθ • Because the magnetic force is always perpendicular to the component of the charge’s velocity perpendicular to the magnetic field, it cannot change its speed. • Force is maximum when the charge is moving perpendicular to the magnetic field ( = 90). • The force is zero if the charge’s velocity is in the same direction as the magnetic field ( = 0). • Also, if the speed is not changing, KE will be constant as well.

4. Example #1 • A positively charged particle traveling at 7.5 x 105 meters per second enters a uniform magnetic field perpendicular to the lines of force. While in the 4.0 x 10-2 tesla magnetic field, a net force of 9.6 x 10-15 newton acts on the particle. What is the magnitude of the charge on the particle?

5. What is the magnetic field (B)? • The magnetic field is a force field just like electric and gravitational fields. • It is a vector quantity. • Hence, it has both magnitude and direction. • Magnetic fields are similar to electric fields in that the field intensity is directly proportional to the force and inversely related to the charge. E = FE/q B = FB/(|q|v) Units for B: N•s/C•m = 1 Tesla

6. Right Hand Rules • Right hand rule is used to determine the relationship between the magnetic field, the velocity of a positively charged particle and the resulting force it experiences.

7. Right Hand Rules #2 #1 #3 FB = |q|v x B

8. V vsinθ Uniform B θ + q The Lorentz Force Equation & RHR FB = qvB sinθ • What is the direction of force on the particle by the magnetic field? • Right b. Left c. Up d. Down • Into the page f. Out of the Page Note: Only the component of velocity perpendicular to the magnetic field (vsin) will contribute to the force.

9. x x x x x x x x x x x x x x x x x x x x x x x x v + Right Hand Rule – What is the Force? What is the direction of the magnetic force on the charge? a) Down b) Up c) Right d)Left

10. Right Hand Rule – What is the Charge? • Particle 1: • Positive • Negative • Neutral • Particle 2: • Positive • Negative • Neutral • Particle 3: • Positive • Negative • Neutral

11. Right Hand Rule – What is the Direction of B • What is the direction of the magnetic field in each chamber? • Up • Down • Left • Right • Into Page • Out of Page 1 4 2 3 • What is the speed of the particle when it leaves chamber 4? • v/2 b. -v • v d. 2v Since the magnetic force is always perpendicular to the velocity, it cannot do any work and change its KE.

12. v1 + x x x x x x x x x x x x v2 + Example 2: Lorentz Force Two protons are launched into a magnetic field with the same speed as shown. What is the difference in magnitude of the magnetic force on each particle? a. F1 < F2 b. F1 = F2 c. F1 > F2 F = qv x B = qvBsinθ Since the angle between B and the particles is 90o in both cases, F1 = F2. How does the kinetic energy change once the particle is in the B field? a. Increase b. Decrease c. Stays the Same Since the magnetic force is always perpendicular to the velocity, it cannot do any work and change its KE.

13. x x x x x x x x x x x x x x x x x x x x x x x x + v Trajectory of a Charge in a Constant Magnetic Field • What path will a charge take when it enters a constant magnetic field with a velocity v as shown below? • Since the force is always perpendicular to the v and B, the particle will travel in a circle • Hence, the force is a centripetal force.

14. x x x x x x x x x x x x x x x x x x x x x x x x + R v Fc Radius of Circular Orbit What is the radius of the circular orbit? Lorentz Force: F = qv x B Centripetal Acc: ac = v2/R Newton’s Second Law: F = mac qvB = mv2/R R = mv/qB

15. Example #2 • A particle with a charge of 5.0 x 10-6 C traveling at 7.5 x 105 meters per second enters a uniform magnetic field perpendicular to the lines of force. The particle then began to move in a circular path 0.30 meters in diameter due to a net force of 1.5 x 10-10 newtons. What is the mass of the particle?

16. Earth’s Magnetosphere • Magnetic field of Earth’s atmosphere protects us from charged particles streaming from Sun (solar wind)

17. Aurora • Charged particles can enter atmosphere at magnetic poles, causing an aurora

18. Crossed Fields in the CRT • How do we make a charged particle go straight if the magnetic field is going to make it go in circles? • Use a velocity selector that incorporates the use of electric and magnetic fields. • Applications for a velocity selector: • Cathode ray tubes (TV, Computer monitor)

19. x x x x x x x x x x x x + + + + + FE FB E - - - - - B into page Phosphor Coated Screen - - - v v v Crossed Fields • E and B fields are balanced to control the trajectory of the charged particle. • FB = FE • Velocity Selector qvB = qE v = E/B

20. Force on a Current Carrying Wire FB = |q|v x B = qvB sinθ (1) Lets assume that the charge q travels through the wire in time t. FB = (q)vBsinθ When t is factored in, we obtain: FB = (q/t)(vt) Bsinθ (2) Where: q/t = I (current) vt = L (length of wire) Equation (2) therefore reduces to: FB = ILB sinθ

21. Examples #2 & #3 • A wire 0.30 m long carrying a current of 9.0 A is at right angles to a uniform magnetic field. The force on the wire is 0.40 N. What is the strength of the magnetic field? • A wire 650 m long is in a 0.46 T magnetic field. A 1.8 N force acts on the wire. What current is in the wire?

22. Torque on a Current Carrying Coil (Electric Motors/Galv.)  = F•r

23. F Direction of Rotation F F  w B I x • -F • x -F -F Max Torque Axis of Rotation Zero Torque x • Torque on a Current Carrying Coil (cont.)

24. Torque on a Current Carrying Coil (cont.) • At zero torque, the magnetic field of the loop of current carrying wire is aligned with that of the magnet. • At maximum torque, the magnetic field of the loop of current carrying wire is at 90o. • The net force on the loop is the vector sum of all of the forces acting on all of the sides. • When a loop with current is placed in a magnetic field, the loop will rotate such that its normal becomes aligned with the externally applied magnetic field.

25. L w Axis of rotation I Torque on a Current Carrying Coil (cont.) • What is the contribution of forces from the two shorter sides (w)? F = IwB sin (90o – ) Note 1: is the angle that the normal to the wire makes with the direction of the magnetic field. Note 2: Due to symmetry, the forces on the two shorter sides will cancel each other out (Use RHR #1). X X X X X X X X

26. Torque on a Current Carrying Coil (cont.) • What is the contribution of torque from the two longer sides (L)? F = BIL for each side since L is always perpendicular to B. The magnitude of the torque due to these forces is:  = BIL (½w sin) + BIL (½w sin) = BILw sin (1) Note: Since Lw = the area of the loop (A), (1) reduces to:  = IAB sin For a winding with N turns, this formula can be rewritten:  = NIAB sin

27. External Magnetic Field – Electromagnet or permanent magnet that provides an attractive and repulsive force to drive armature. Split Ring Commutator – Brushes and split ring that provide the electrical connection to the armature from the external electrical source. Armature – Part of the motor that spins that contains windings and an iron core. DC Motor DC Electric Motor

28. Key Ideas • Lorentz Force: A charge moving perpendicular to a magnetic field will experience a force. • Charged particles moving perpendicular to a magnetic field will travel in a circular orbit. • The magnetic force does not change the kinetic energy of a moving charged particle – only direction. • The magnetic field (B) is a vector quantity with the unit of Tesla • Use right hand rules to determine the relationship between the magnetic field, the velocity of a positively charged particle and the resulting force it experiences.