Electricity PDF

Electricity 1. Fundamentals of electricity: electric charge, electric field, electric potential. 2. Electrophoresis of proteins. 3. Electric dipole 4. Electric current. Basics. 5. Electric current in electrolytes. 6. Electric current in living tissues. 7. Electr...

Electricity 1. Fundamentals of electricity: electric charge, electric field, electric potential. 2. Electrophoresis of proteins. 3. Electric dipole 4. Electric current. Basics. 5. Electric current in electrolytes. 6. Electric current in living tissues. 7. Electric shock, physiological effects of current. 8. Electricity in gases. 1 Fundamentals of electricity Electricity is an apparent force in nature that exists whenever there is a net electrical charge between any two objects. Electric charge is a physical property of elementary particles of atom. Although charge can be positive or negative, the magnitude of charge is always quantized. Magnitude of elementary (smallest) charge is e= 1.610-19 C. So any charge q can be expressed by q=ne, where n – any natural number. The SI unit of charge is called the coulomb, abbreviated C. In the atom protons are positively charged and electrons are charged negatively. Two like charges repel each other. Positive and negative charges attract each other. When there are equal numbers of positive and negative charges there is no electrical force as there is no net charge. This is the case for a neutral atom. Electrical charge is conserved; charge is neither created nor destroyed. When electrons are transferred from one material to another (e.g. rubbing a wool cloth with a plastic comb) electrical force is created. Coulomb’s law describes the electrostatic force F between two charged particles q1 and q2 separated by distance r: 1 q1 q 2 qq F  k 1 22 4 0 r 2 r where 0 is the permittivity constant of vacuum, defined as 0=8.8510-12 F/m (or C2N-1 m-2), k=9109Nm2C-2. If we have any other medium instead of vacuum, permittivity constant of the medium  must be included: 1 q1 q 2 qq F  k 1 22 4 0  r 2 r Electric field E defines the electric force exerted on a positive unit charge positioned within any given space. F E q0 When we have several sources of electric field E1, E2, … superposition principle can be applied: E  E1  E 2   It means that resultant electric field is equal to the vector sum of individual electric fields. Electric field lines make a visual display of electric field that uses imaginary lines to represent the magnitude and direction of the electric field. Lines go away from positive charge and go towards negative charge. 2 Potential energy can be defined as the capacity for doing work, which arises, from position or configuration. In the electrical case, a charge will exert a force on any other charge. So potential energy arises from any collection of charges. For example, if a positive charge is fixed at some point in space, any other positive charge, which is brought close to it, will experience a repulsive force and will therefore have potential energy. Its potential energy Wp is defined as amount of work required to move a charge q from an infinite distance to its final position within electric field E. Electric potential  at any point of electrostatic field E is defined as the potential energy Wp per unit charge at the point: Wp  q For the point charge, its potential at any point of free space will be expressed as: q  k r Usually we can measure electric potential difference  between two points in electrostatic field. It represents the work required to move a unit charge from one point to another. The potential distribution in an electric field can be represented graphically by equipotential lines. These are lines such that potential has the same value at all points of the line. Equipotential lines always are perpendicular to electric field lines. Units of potential and potential difference are V. Measured potential difference is also called voltage V. 3 Relationship between electric field and voltage is as follows: d E dr In other words electric field is equal to the negative of potential gradient in the direction of field. When we can measure potential difference  and distance r between two points an approximate relationship could be used:  E r Electrophoresis of proteins The term electrophoresis describes the transport of charged macromolecules (proteins or DNA) through electrolyte under an applied voltage. This is a basic laboratory tool in biochemistry. In biological applications electrophoresis is used to characterize various objects ranging from bacteria or viruses to globular proteins or DNA. This is possible due to these objects’ net electric charge. This tool has found important clinical and diagnostic applications intended to separate various components (e.g. proteins in blood plasma). As a result abnormal patterns of blood composition can be identified through electrophoresis. Proteins are folded polymers composed from amino acids arranged in multitude of possible sequences. Sequence variations lead to different folding patterns and consequently, functional properties in the body. The net charge of the protein may vary from –100 to +100 elementary charges and is largely determined by the pH value of the solution in which a given protein is suspended. A charged protein with a total electric charge q is subjected to the electric force: Fe=qE, where E is applied electric field. Another force acting to the protein is drag force because viscosity of the medium Fd=-6av,  - viscosity, v – velocity of the migrating protein, a - radius of protein. Two forces must compensate each other: 4  Fe=Fd qE=-6av v=-qE/6a vq. It means that for particles of the same size the distance traveled over a given time is proportional to electric charge of the particle. In other words particles (or proteins) having different charges will travel different distances during given time and will be separated from each other. Fig. Example of gel electrophoresis Electric dipole An electric dipole is a system of two equal and opposite point charges separated by a small distance. The extended straight line joining the two point charges in a dipole is called the dipole axis. The electric dipole moment for a pair of opposite charges of magnitude q is defined as the 5 magnitude of the charge times the distance d between them and the defined direction is toward the positive charge:   p  qd d -q +q The electric field and potential of an electric dipole can be found by superposing the point charge potentials of the two charges: Electric field (solid) and equipotential (dashed) lines of an electric dipole: Many molecules (water, sodium chloride, etc.) can have an electric dipole moment. Dipole as a model is useful in biomedical description of electric fields, generated by single cells or organs. Dipole is a good model for description of generation of cardiogram. 6 Electric current. Basics So far we discussed mainly static (not moving) charges. When charged particles are moving we can talk about electric current. Where there is a net flow of charge across any area, we say there is a current across the area. Current across the area is defined as the net charge transferred across the area per unit time: I=q/t Unit of current is called ampere (A). 1A=1C/1s. When charges flow continuously (I=const) only in one direction around a circuit, the current is called direct current (DC). I I0 t When direction of charge flow changes from moment to moment, the current is called alternating current (AC). I t We can define pulse current, when current strength changes during time. I t Current per unit cross-sectional area is called the current density j: dI j dS 7 dI is current through the small surface area dS. Another expression of current density is   j  qnv q – charge of a particle, n – number of particles, v – velocity charged particles. When we have many kinds of charged particles   j   qi ni vi i In a conductor (metal) charge is transferred by electrons. In liquids and gases charge is transferred by ions. Electric current in electrolytes Human body is filled with electrolytes. The relationship between the electric field E and the electrolytic current I is: E=IR R is the resistance of electrolytic cell or volume. If two poles of the cell are in the form of two parallel plates spaced by a distance l apart, then the resistance is given by R=l/S S - cross section of plates,  - the resistivity of the electrolyte. The typical order of magnitude of the resistivity for body fluids is about 1m. This is nine orders of magnitude larger than the resistivity of copper, so electrical conduction by ions is less effective than electrical conduction by electrons. 8 For electrolytic conductance the electric force F=qE, applied to the ion is balanced by the Stokes friction Fd=6rv. Consequently velocity can be computed as q v E 6r or v=E  is called electrophoretic mobility of ions: =q/6r Actually mobility is defined as velocity of electric particle under the unit electric field. Mobility depends on electric charge, size of the ion and viscosity of the solution. We already know that   j   qi ni vi i For electrolyte composed of positive and negative ions of the same salt is true: j=qn+v++qn-v- Taking into account mobility, we can rewrite : j=qnE(++-) Electric current in living tissues Conductance  of the tissue is expressed as =1/. Various tissues of living organism have different conductance to the electric current. Some are of high conductance, others are of medium conductance, and some are of low conductance. Those of good conductance are organic fluids containing dissolved ions – blood, spinal liquid, and urine. Medium conductance is characteristic to internal organs and muscle tissues. While bones and dry skin are of low conductance. Some examples of resistivities: Spinal liquid 0.55 m Blood 1.66 m Muscle tissue 2 m Brain tissue 14.3 m Dry skin 105 m Bone 107 m Living organisms in general have high electric resistance. It is possible to say that high resistance of a living tissue is due to its capacitance and ohmic resistance. The total resistance to the current is called impedance (Z): 1 Z 1 2  (C ) 2 R 9 The tissue impedance value depends on blood supply and can be informative for diagnostic reasons. The method is called rheography. Small alternating current (AC) of frequency 20-30 kHz is used. Rheograms of various organs (heart, kidney, liver etc.) could be acquired. If the nerves in any region are damaged or if there is a carcinoma or other kind of tumor compressing nerves, resistance increases noticeably near this position. Physiological effects of current, electric shock The severity of electric shock depends on many factors. The most dominant is amount of current passing through the person. The effect of a shock also depends on the path the current takes, the duration of shock, and whether the current is ac or dc. In case of ac there is a dependence of the frequency. Physiological effects of electric shock as a function of current on the assumption that duration of shock is 1s, and is caused by 50 Hz current: Current (mA) Effect 1 Threshold of sensation 5 Maximum harmless current 10-20 Onset of sustained muscular contraction; can’t let go for duration of shock; contraction of chest muscles may stop breathing during shock (fatal if continued) 50 Onset of pain heart still unaffected 100-300+ Ventricular fibrillation possible; very often fatal 300 Onset of burns (thermal hazard); depends on concentration of current 6000 (6A) Onset of sustained ventricular contraction and respiratory paralysis; both stop when shock is over; heartbeat often returns to normal These values are for male subjects. For females these values are 60% to 80% of those listed in a table. At a current of 1 mA the sensation of being shocked becomes noticeable. Somewhat higher currents can cause muscles to contract involuntarily. The reason muscles contract is that nerves controlling muscles start sending electrical signals. If you grasp the wire by your hand, hand will be unable to release the wire. The leading cause of death from electrical shock is ventricular fibrillation, an irregular, and uncoordinated beating of heart. The victim dies from lack of blood circulation. Interestingly we can stop ventricular fibrillation passing much higher current through the heart. Here we did not mention dangerous voltages. This is because the severity of shock depends on current and not directly of voltage. According to Ohm’s law: I=V/R So current depends on a combination of voltage and resistance. 10 The human body is a conductor whose combined resistance is approximately 1500 when dry. When the body becomes wet, the resistance is reduced to about 500. If we assume the voltage source is at 120 V, the current through the dry body is via Ohm’s law: I=V/R=120V/1500= 80mA When the body is wet, I=120V/500= 240mA As we see, ventricular fibrillation can occur at currents of 100 mA, so the harmful effects of exposure to electricity, particularly if the electrical contact is wet, become quite clear. Frequency effects. The body is most sensitive to electrical shock at frequencies close to 50- 60Hz. Possibly it is because this is similar to the firing frequency of many nerves. Nerves and muscles of the body are less sensitive at both higher and lower frequencies. The effects of high frequency shocks are mostly thermal. A large high frequency current may cause burns but is less likely to cause ventricular fibrillation. Because of this high frequency currents are used in electrosurgery. Electricity in gases In most cases gas consists of electrically neutral molecules. So conductance to electric current of such gas is equal to zero. Only in high temperatures or very strong electric fields electrons are “stripped” from atoms or molecules. This state is called plasma. Plasma allows the conduction of electricity, forming a spark, arc, or lightning. Electrical conduction in plasma is due to the motion of both the electrons and the positively charged ions. Some factors such as sunshine beam, X-rays, cosmic radiation could raise the ionization of gas and it becomes conductive to electric current too. There are always some small amounts of gaseous ions in surrounding space. In normal pollutant-free air there are 1500 to 4000 ions/cm3. These ions are called aeroions. Negative and positive ions in the air have different effect to our well being. Negative ions can destroy harmful bacteria – positive contribution. Positive ions (e.g. from TV screen) usually induce discomfort (depression, nausea, irritability, migraine, and asthma). These disturbances can be counteracted with the effect of negative ions. Size of ions is very important, because only small negative ones can be inhaled and exert their positive biological effect. Negative ions are destroyed by pollution and dust (in most cases heavy particles). Artificially generated aeroions can be used for treatment of patients or indoor spaces. This procedure is called aeroionotheraphy. Sometimes so called “electrostatic shower” is used. In this case aeroionization is provided by means of strong electric field generated by high voltage (up to 50kV). 11