2. 1 Magnetic properties of bioobjects. Electromagnetic waves in biological environments. Interaction environment field with biological tissue.

3. 2 Plan Magnetic Field Flux Density Magnetic Force on Moving Charge Direction of Magnetic Force Electromagnetic Fields Biot-Savart Law Electrophoresis Electromagnetic Waves Poynting Vector Intensity of EM Wave

4. 3 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. N S Bar Magnet N S

5. 4 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 S poles. NS N E W S N Compass Bar magnet S N Iron filings

6. 5 Magnetic Field Lines NS 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. 6 Magnetic Field A bar magnet has a magnetic field around it. This field is 3D in nature and often represented by lines LEAVING north and ENTERING south To define a magnetic field you need to understand the MAGNITUDE and DIRECTION We sometimes call the magnetic field a B-Field as the letter “B” is the SYMBOL for a magnetic field with the TESLA (T) as the unit.

8. 7 Facts about Magnetism Magnets have 2 poles (north and south) Like poles repel Unlike poles attract Magnets create a MAGNETIC FIELD around them

9. 8 Magnetic Flux Density  Magnetic Flux density: AA Magnetic flux lines are continuous and closed.Magnetic flux lines are continuous and closed. Direction is that of the B vector at any point.Direction is that of the B vector at any point. Flux lines are NOT in direction of force but.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. 9 Calculating Flux Density When Area is Not Perpendicular The flux penetrating the area A when the normal vector n makes an angle of  with the B-field is: The angle  is the complement of the angle a that the plane of the area makes with the B field. (Cos  = Sin  n A   B

11. 10 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 pole has 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. + E + B v v 

12. 11 Magnetic Force on Moving Charge NS B N Imagine a tube that projects charge +q with velocity v into perpendicular B field. Upward magnetic force F on charge moving in B field. vF Experiment shows: 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.

13. 12 Magnetic Force on a moving charge If a MOVING CHARGE moves into a magnetic field it will experience a MAGNETIC FORCE. This deflection is 3D in nature. N N S S - vovo B The conditions for the force are: Must have a magnetic field present Charge must be moving Charge must be positive or negative Charge must be moving PERPENDICULAR to the field.

14. 13 Direction of Magnetic Force B vF NSN The right hand rule: 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. The force is greatest when the velocity v is perpendicular to the B field. The deflection decreases to zero for parallel motion. B v F

15. 14 Force and Angle of Path SNNS NN SNN Deflection force greatest when path perpendicular to field. Least at parallel. B v F v sin  v 

16. 15 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: Magnetic Field Intensity B: 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).

17. 16 Example 1. A 2-nC charge is projected with velocity 5 x 10 4 m/s at an angle of 30 0 with a 3 mT magnetic field as shown. What are the magnitude and direction of the resulting force? v sin  v   B v F Draw a rough sketch. q = 2 x 10 -9 C v = 5 x 10 4 m/s B = 3 x 10 -3 T  = 30 0 Using right-hand rule, the force is seen to be upward. Resultant Magnetic Force: F = 1.50 x 10 -7 N, upward B

18. 17 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. NSNNSN B v F Right-hand rule for positive q F Bv Left-hand rule for negative q

19. 18 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 One way of indicating the directions of fields perpen- dicular to a plane is to use crosses X and dots  : X X X X X X X X X X X X X X X X  A field directed into the paper is denoted by a cross “X” like the tail feathers of an arrow. A field directed out of the paper is denoted by a dot “ ” like the front tip end of an arrow. 

20. 19 Practice With Directions: 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  What is the direction of the force F on the charge in each of the examples described below? -v - v +v v + UpF LeftF F Right UpF negative q

21. 20 Crossed E and B Fields The motion of charged particles, such as electrons, can be controlled by combined electric and magnetic fields. x x x x + - e-e- v Note: F E on electron is upward and opposite E-field. But, F B on electron is down (left-hand rule). Zero deflection when F B = F E B v FEFEFEFE Ee-e- - Bv FBFBFBFB -

22. 21 The Velocity Selector This device uses crossed fields to select only those velocities for which F B = F E. (Verify directions for +q) x x x x + - +q v Source of +q Velocity selector When F B = F E : By adjusting the E and/or B-fields, a person can select only those ions with the desired velocity.

23. 22 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 10 6 m/s. What is the electric field E? x x x x + - +q v Source of +qV E = vB E = (1.5 x 10 6 m/s)(20 x 10 -3 T); E = 3.00 x 10 4 V/m

24. 23 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. 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 + + + + Centripetal F c = F B R FcFcFcFc The radius of path is:

25. 24 Mass Spectrometer +q R + - x x x x x x x x x x x x x x x x x x x x x Photographic plate m1m1 m2m2 slit 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:

26. 25 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 +q R + - x x x x Photographic plate m slit 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

27. 26 Summary NSN B v F Right-hand rule for positive q NSN F Bv Left-hand rule for negative q 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.

28. 27 Summary (Continued) B v F v sin  v  For a charge moving in a B-field, the magnitude of the force is given by: F = qvB sin 

29. 28 Summary (Continued) x x x x + - +q+q v V The velocity selector: +q R + - x x x x m slit x x x x x x x x x x x x x The mass spectrometer:

30. 29 Electromagnetic Fields Electromagnetics is the study of the effect of charges at rest and charges in motion. Some special cases of electromagnetics:  Electrostatics: charges at rest  Magnetostatics: charges in steady motion (DC)  Electromagnetic waves: waves excited by charges in time-varying motion

31. 30 Electromagnetic Fields A scalar is a quantity having only an amplitude (and possibly phase). A vector is a quantity having direction in addition to amplitude (and possibly phase). Examples: voltage, current, charge, energy, temperature Examples: velocity, acceleration, force

32. 31 Electromagnetic Fields Fundamental vector field quantities in electromagnetics:  Electric field intensity  Electric flux density (electric displacement)  Magnetic field intensity  Magnetic flux density units = volts per meter (V/m = kg m/A/s 3 ) units = coulombs per square meter (C/m 2 = A s /m 2 ) units = amps per meter (A/m) units = teslas = webers per square meter (T = Wb/ m 2 = kg/A/s 3 )

33. 32 Universal constants in electromagnetics:  Velocity of an electromagnetic wave (e.g., light) in free space (perfect vacuum)  Permeability of free space  Permittivity of free space:  Intrinsic impedance of free space:

34. 33 Electromagnetic Fields In free space: Relationships involving the universal constants:

35. 34 Electromagnetic Fields in Materials In a simple medium, we have: (independent of field strength) linear (independent of field strength) (independent of position within the medium) isotropic (independent of position within the medium) (independent of direction) homogeneous (independent of direction) (independent of time) time-invariant (independent of time) non-dispersive (independent of frequency)

36. 35 Electromagnetic Fields in Materials  = permittivity =  r  0 (F/m)  = permeability =  r  0 (H/m)  = electric conductivity =  r  0 (S/m)  m = magnetic conductivity =  r  0 (  /m)

37. 36 Biot-Savart Law The Biot-Savart Law relates magnetic fields to the currents which are their sources. In a similar manner, Coulomb's law relates electric fields to the point charges which are their sources. Finding the magnetic field resulting from a current distribution involves the vector product, and is inherently a calculus problem when the distance from the current to the field point is continuously changing.magnetic fieldscurrentsCoulomb's lawelectric fieldsvector product See the magnetic field sketched for the straight wire to see the geometry of the magnetic field of a current.straight wire Magnetic field of currerent element where dL- infinitesmal length of conductor carrying electric current I, r - unit vector to specify direction of the vector distance r from the current to the field point.

38. 37 Electrophoresis is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. This electrokinetic phenomenon was observed for the first time in 1807 by Reuss, who noticed that the application of a constant electric field caused clay particles dispersed in water to migrate. It is ultimately caused by the presence of a charged interface between the particle surface and the surrounding fluid.dispersed particleselectric field electrokinetic phenomenonelectric fieldclaywater

39. 38 The dispersed particles have an electric surface charge, on which an external electric field exerts an electrostatic Coulomb force. According to the double layer theory, all surface charges in fluids are screened by a diffuse layer of ions, which has the same absolute charge but opposite sign with respect to that of the surface charge. electric surface charge electrostaticCoulomb forcedouble layerdiffuse layer The electric field also exerts a force on the ions in the diffuse layer which has direction opposite to that acting on the surface charge. This latter force is not actually applied to the particle, but to the ions in the diffuse layer located at some distance from the particle surface, and part of it is transferred all the way to the particle surface through viscous stress. This part of the force is also called electrophoretic retardation force.diffuse layersurface chargeionsviscousstress

40. 39 Electromagnetic Waves It consists of mutually perpendicular and oscillating electric and magnetic fields. The fields always vary sinusoidally. Moreover, the fields vary with the same frequency and in phase (in step) with each other. The wave is a transverse wave, both electric and magnetic fields are oscillating perpendicular to the direction in which the wave travels. The cross product always gives the direction in which the wave travels. Electromagnetic waves can travel through a vacuum or a material substance. All electromagnetic waves move through a vacuum at the same speed, and the symbol c is used to denote its value. This speed is called the speed of light in a vacuum and is: The magnitudes of the fields at every instant and at any point are related by

41. 40 Properties of the Wave Wavelength λ is the horizontal distance between any two successive equivalent points on the wave. Amplitude A is the highest point on the wave pattern. Period T is the time required for the wave to travel a distance of one wavelength. Unit is second. Frequency f : f=1/T. The frequency is measured in cycles per second or hertz (Hz). Speed of wave is v=λ/T= λf

42. 41 Poynting Vector The rate of energy transport per unit area in EM wave is described by a vector, called the Poynting vector The direction of the Poynting vector of an electromagnetic wave at any point gives the wave's direction of travel and the direction of energy transport at that point. The magnitude of S is

43. 42 Intensity of EM Wave The time-averaged value of S is called the intensity I of the wave the root-mean-square value of the electric field, as The root-mean-square value of the electric field, as The energy associated with the electric field exactly equals to the energy associated with the magnetic field.