Chapter 29 - Magnetic Fields

1. Chapter 29 - Magnetic Fields A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007

2. Objectives: After completing this module, you should be able to: • Define the magnetic field, discussing magnetic poles and flux lines. • Solve problems involving the magnitude and direction of forces on charges moving in a magnetic field. • Solve problems involving the magnitude and direction of forces on currentcarrying conductors in a B-field.

3. S Bar Magnet N S N Magnetism Since ancient times, certain materials, called magnets, have been known to have the property of attracting tiny pieces of metal. This attractive property is called magnetism.

4. Iron filings N S W N S N E S N Bar magnet Compass Magnetic Poles The strength of a magnet is concentrated at the ends, called north and south “poles” of the magnet. A suspended magnet: N-seeking end and S-seeking end are N and Spoles.

5. N S S N N S S N N S Magnetic Attraction-Repulsion Magnetic Forces: Like Poles Repel Unlike Poles Attract

6. N S Magnetic Field Lines We can describe magnetic field lines by imagining a tiny compass placed at nearby points. The direction of the magnetic field B at any point is the same as the direction indicated by this compass. Field B is strong where lines are dense and weak where lines are sparse.

7. N N N S Field Lines Between Magnets Unlike poles Attraction Leave N and enter S Repulsion Like poles

8. Magnetic field flux lines f Electric field DN Df DA DA S N Line density Line density The Density of Field Lines Magnetic Field B is sometimes called the flux density in Webers per square meter (Wb/m2).

9. Df DA Magnetic Flux density: Magnetic Flux Density • Magnetic flux lines are continuous and closed. • Direction is that of the B vector at any point. • Flux lines are NOT in direction of force but ^. When area A is perpendicular to flux: The unit of flux density is the Weber per square meter.

10. n A q a B Calculating Flux Density When Area is Not Perpendicular The flux penetrating the area A when the normal vector n makes an angle of q with the B-field is: The angle q is the complement of the angle a that the plane of the area makes with the B field. (Cos q = Sin a)

11. E + + ^ B v v Origin of Magnetic Fields Recall that the strength of an electric field E was defined as the electric force per unit charge. Since no isolated magnetic polehas ever been found, we can’t define the magnetic field B in terms of the magnetic force per unit north pole. We will see instead that magnetic fields result from charges in motion—not from stationary charge or poles. This fact will be covered later.

12. F v B N N S Experiment shows: Magnetic Force on Moving Charge Imagine a tube that projects charge +q with velocity v into perpendicular B field. Upward magnetic force F on charge moving in B field. Each of the following results in a greater magnetic force F: an increase in velocityv, an increase in chargeq, and a larger magnetic field B.

13. The right hand rule: F F B B With a flat right hand, point thumb in direction of velocity v, fingers in direction of B field. The flat hand pushes in the direction of force F. v v N N S Direction of Magnetic Force The force is greatest when the velocity v is perpendicular to the B field. The deflection decreases to zero for parallel motion.

14. N N N N N N S S S F B q v sin q v v Force and Angle of Path Deflection force greatest when path perpendicular to field. Least at parallel.

15. Magnetic Field Intensity B: Definition of B-field Experimental observations show the following: By choosing appropriate units for the constant of proportionality, we can now define the B-field as: A magnetic field intensity of one tesla (T) exists in a region of space where a charge of one coulomb(C) moving at 1 m/s perpendicular to the B-field will experience a force of one newton (N).

16. F B B 300 v sin f v v Example 1.A 2-nC charge is projected with velocity 5 x 104 m/s at an angle of 300 with a 3 mT magnetic field as shown. What are the magnitude and direction of the resulting force? Draw a rough sketch. q = 2 x 10-9 C v = 5 x 104 m/s B = 3 x 10-3 T q= 300 Using right-hand rule, the force is seen to be upward. Resultant Magnetic Force: F = 1.50 x 10-7 N, upward

17. B v F Right-hand rule for positive q F Left-hand rule for negative q B v N N S N N S Forces on Negative Charges Forces on negative charges are opposite to those on positive charges. The force on the negative charge requires a left-hand rule to show downward force F.

18. A field directed into the paper is denoted by a cross “X” like the tail feathers of an arrow. X X X X X X X X X X X X X X X X · · · · A field directed out of the paper is denoted by a dot “ ” like the front tip end of an arrow. · · · · · · · · · · · · · Indicating Direction of B-fields One way of indicating the directions of fields perpen-dicular to a plane is to use crosses X and dots · :

19. F F v X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Up Up v F + Left + - · · · · · · · · · · · · · · · · v F · · · · · · · · Right - · · · · · · · · v Practice With Directions: What is the direction of the force F on the charge in each of the examples described below? negative q

20. + e- x x x x x x x x v - B FE B - - v v E e- FB Crossed E and B Fields The motion of charged particles, such as electrons, can be controlled by combined electric and magnetic fields. Note:FEon electron is upwardand opposite E-field. But, FBon electron is down(left-hand rule). Zero deflection when FB = FE

21. Source of +q + +q x x x x x x x x v - Velocity selector The Velocity Selector This device uses crossed fields to select only those velocities for which FB = FE. (Verify directions for +q) When FB = FE : By adjusting the E and/or B-fields, a person can select only those ions with the desired velocity.

22. Source of +q + +q x x x x x x x x v - V Example 2. A lithium ion, q = +1.6 x 10-16 C, is projected through a velocity selector where B = 20 mT. The E-field is adjusted to select a velocity of 1.5 x 106 m/s. What is the electric field E? E = vB E = 3.00 x 104 V/m E = (1.5 x 106 m/s)(20 x 10-3 T);

23. X X X X X X 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 Fc Circular Motion in B-field The magnetic force F on a moving charge is always perpendicular to its velocity v. Thus, a charge moving in a B-field will experience a centripetal force. Centripetal Fc = FB The radius of path is:

24. +q x x x x x x x x - + Photographic plate R x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x slit m2 m1 Mass Spectrometer Ions passed through a velocity selector at known velocity emerge into a magnetic field as shown. The radius is: The mass is found by measuring the radius R:

25. +q x x x x x x x x - + Photographic plate R x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x slit m Example 3.A Neon ion, q = 1.6 x 10-19 C, follows a path of radius 7.28 cm. Upper and lower B = 0.5 T and E = 1000 V/m. What is its mass? v = 2000 m/s m = 2.91 x 10-24 kg

26. B v F Right-hand rule for positive q F Left-hand rule for negative q B v N N S N N S Summary The direction of forces on a charge moving in an electric field can be determined by the right-hand rule for positive charges and by the left-hand rule for negative charges.

27. F B q v sin q v v Summary (Continued) For a charge moving in a B-field, the magnitude of the force is given by: F = qvB sin q

28. + +q x x x x x x x x v - V +q x x x x x x x x - + R x x x x x x x x x x x x x x x x x x x x x x x x x x slit m Summary (Continued) The velocity selector: The mass spectrometer:

29. CONCLUSION: Chapter 29Magnetic Fields