1. ECEN5341/4341Bioelectromagnetics Spring 2015 Frank S. Barnes Contact Info: (303)492-8225 frank.barnes@colorado.edu ECOT 250 http://ecee.colorado.edu/~ecen4341/5341 index.html 1

2. Lecture 2 ECEN 4341/5341 Spring 2015 Some Background E+M Theory and some relative sizes of effects for the interaction between electric and magnetic fields and atomic systems. 2

3. Voltage and Electric Fields +.V 3

4. Low Frequency Fields 1 4

5. Electromagnetic Fields Near a Dipole Near E Fields Near H Field H is the height of the dipole, k is the propagation constant k=2π/λ, is the angular frequency is the wave impedance r is the distance from the radiating element Radiated field Induced E Field 5

6. Results for Low Frequencies 1 Almost all the fields are static or induced 2. At 60Hz fields with in a few km the radiated fields are orders of magnitude smaller than the static or induced fields. 3. Heating from radiated fields is very small at low frequencies but not at RF. 6

7. 1 At DC the Parallel Components Tangential components For AirFor tissue So that for a wave from air to tissue And θ 2 is nearly 0 so that E 1 is nearly perpendicular and E 2 is nearly parallel to the surface. The perpendicular Components The penetration of DC Electric Fields from Air to Tissue 7

8. Low Frequency Field Penetration from Air to Tissue Boundary conditions for incident wave with the E field Where is the surface charge density For tissue at very low frequencies At 60Hz this gives So the induced field inside the body is very small for reasonable external fields!! 8

9. Low Frequency E Field Penetration from Air to Tissue For DC For 60 Hz This says that the high conductivity and dielectric constants of tissue basically shield the body from external low frequency electric fields. However you need to be more careful if you look at skin and the sensory nerves near the surface. 9

10. Low Frequency Magnetic Field Effects 1. Orientation of ferromagnetic particles – Fe 3 O 4 in birds, fish and possibly Humans 2. Orientation of diamagnetically or paramagnetically anisotropic molecules and cellular elements 3. Generation of potential differences at right angles to a stream of moving ions (Hall effect, also sometimes called a magnetohydrodynamic effect) as a result of the magnetic force F m =¼ qvB sin θ, where q is the electric charge, v is the velocity of the charge, B is the magnetic flux density, and sin θ is the sine of the angle θ between the directions v and B. One well-documented result of this mechanism is a ‘‘spike’’ in the electrocardiograms of vertebrates subjected to large dc H fields. 10

11. Low Frequency Magnetic Field Effects 4. Shifts in Energy of Atomic and Molecular States, Zeeman shifts in electron energies and hyperfine splitting of nuclear energy levels. – This effects things like free radical lifetimes and concentrations, metabolic processes in things like hemoglobin and chlorophyll 5. Induction of E fields with resulting electrical potential differences and currents within an organism by rapid motion through a large static H field. Some magnetic phosphine's are due to such motion 11

12. Field Required to get 10mV/m vs frequency for air to muscle 1 External E and H field required to obtain an internal E field of 10 mV/m (conductivity and dielectric permittivity for skeletal muscle from Foster, K.R., Schepps, J.L., and Schwan, H.P. 1980. Biophys. J., 29:271–281. H-field calculation assumes a circular path of 0.1-m radius perpendicular to magnetic flux). 12

13. Reflection and Transmission at Plain Boundary for Perpendicular Incidence 1 13

14. Transmission for E Parallel vs Frequency Skeletal Muscle FIGURE 0.8 External E and H field required to obtain an internal E field of 10 mV=m (conductivity and dielectric permittivity for skeletal muscle from Foster, K.R., Schepps, J.L., and Schwan, H.P. 1980. Biophys. J., 29:271–281. H-field calculation assumes a circular path of 0.1-m radius perpendicular to magnetic flux). 14

15. Depth of Penetration 1. For a good conductor,Skin Depth 2. A good conductor means a large ratio of conduction current J =σ E to displacement current or 15

16. More General Skin Depth 1. Most biological materials are not good conductors (0.1 < p < 10) and we need a more general expression. 16

17. Ratio of Transmitted to Reflected Power For Perpendicular Incidence at Air Muscle Interface. 1 17

18. Transmission and Reflection 1 The reflection coefficient 2. The Transmission coefficient 18

19. Some Values for Coefficients for Muscle 19

20. The Wave Impedances η = E/H 1. Homogenous Medium 2. For Air or Vacuum 20

21. Transmitted and Reflected Power 1 R mean the real part of η 2. η * Means complex conjugate of η 2, =1- 1- 21

22. Skin Depth for Plane Wave vs Frequency for Muscle Electromagnetic skin depth in muscle tissue from plane wave expression (Equation 0.19, Table 0.1). 22

23. Power Transmitted 23

24. Waves at an Angle 1 24

25. Generalize Snell’s Law 25

26. Transmission as Function of Angle Electromagnetic skin depth in muscle tissue from plane wave expression (Equation 0.19, Table 0.1). 26

27. Frequency, Wave Length, Energy in Electron Volts (eV) 1 27

28. Bond Strengths and Thermal Energy 28