Chapter 29 - Magnetic FieldsA PowerPoint Presentation byPaul E. Tippens, Professor of PhysicsSouthern Polytechnic State University 2007

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 current carrying conductors in a B-field.

MagnetismSince 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.

Magnetic PolesThe 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 S poles.

Magnetic Attraction-RepulsionMagnetic Forces: Like Poles RepelUnlike Poles Attract

Magnetic Field LinesWe 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.

Field Lines Between MagnetsUnlike polesLike polesLeave N and enter SAttractionRepulsion

The Density of Field LinesMagnetic Field B is sometimes called the flux density in Webers per square meter (Wb/m2).

Magnetic Flux DensityMagnetic 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.

Calculating Flux Density When Area is Not PerpendicularThe 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)

Origin of Magnetic FieldsRecall that the strength of an electric field E was defined as the electric force per unit charge.Since no isolated magnetic pole has ever been found, we cant 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 motionnot from stationary charge or poles. This fact will be covered later.

Magnetic Force on Moving ChargeImagine 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 velocity v, an increase in charge q, and a larger magnetic field B.

Direction of Magnetic ForceThe force is greatest when the velocity v is perpendicular to the B field. The deflection decreases to zero for parallel motion.

Force and Angle of PathDeflection force greatest when path perpendicular to field. Least at parallel.

Definition of B-fieldExperimental 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).

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 = 300Using right-hand rule, the force is seen to be upward.Resultant Magnetic Force: F = 1.50 x 10-7 N, upward

Forces on Negative ChargesForces 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.

Indicating Direction of B-fieldsOne way of indicating the directions of fields perpen-dicular to a plane is to use crosses X and dots :

Practice With Directions:What is the direction of the force F on the charge in each of the examples described below?negative q

Crossed E and B FieldsThe motion of charged particles, such as electrons, can be controlled by combined electric and magnetic fields.Note: FE on electron is upward and opposite E-field.But, FB on electron is down (left-hand rule).Zero deflection when FB = FE

The Velocity SelectorThis 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.

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 = vBE = (1.5 x 106 m/s)(20 x 10-3 T);E = 3.00 x 104 V/m

Circular Motion in B-fieldThe 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 = FBThe radius of path is:

Mass SpectrometerIons 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:

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/sm = 2.91 x 10-24 kg

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.

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

Summary (Continued)The velocity selector:The mass spectrometer:

CONCLUSION: Chapter 29Magnetic Fields