ECEN5341/4341 Spring 2019 Lecture 2 January 16,2019

Radiation . The power radiated from a charged q is given by Where a is the acceleration and c is the velocity of light For a short wire power radiated is given by η Is the impedance of free space The difference between induced fields and radiation depends on the dimensions of the device and the wave length. At 60Hz the wavelength is given by The radiation resistance for short linear dipoles of length l <<λ is given by The radiated power is given by

Maxwell’s Equations 1 2. Another Form where 𝜌 is the charge density

Electromagnetic Fields Near a Dipole Radiated field Near H Field Near E Fields Induced E Field Radiated 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

Low Frequency Induced E Fields 1 2. For a cylinder Faraday’s Generator

Boundary Conditions

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.

The penetration of DC Electric Fields from Air to Tissue 1 The penetration of DC Electric Fields from Air to Tissue At DC the Parallel Components The perpendicular Components Tangential components For Air For tissue So that for a wave from air to tissue And θ2 is nearly 0 so that E1 is nearly perpendicular and E2 is nearly parallel to the surface.

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 E field inside the body is very small for reasonable external E fields!!

Low Frequency 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.

Low Frequency Magnetic Field Effects 1. Orientation of ferromagnetic particles Fe3O4 in bacteria, birds , fish and possibly Humans 2. Orientation of diamagnetic or paramagnetic 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 magneto-hydrodynamic effect) as a result of the magnetic force Fm =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.

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 free radical lifetimes and concentrations, metabolic processes in 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

Field Required to get 10mV/m vs frequency for air to muscle 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).

EM Waves at a Plane Boundary

Electric Fields and Dielectric Sphere

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).

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

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

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

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

Some Values for Coefficients for Muscle

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

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

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).

Power Transmitted

Waves at an Angle 1

Generalize Snell’s Law

Transmission as Function of Angle Electromagnetic skin depth in muscle tissue from plane wave expression (Equation 0.19, Table 0.1) at 10MHz.

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

Bond Strengths and Thermal Energy