RMI 213: Principles of Medical Imaging Lecture 5 - Electricity and Magnetism PDF

RMI 213 Principles of medical imaging Lecture 5 Electricity and Magnetism Slide 1 fchs.ac.ae Learning Outcomes At the conclusion of this lecture, associated tutorial and practical session (if relevant), you will be able to: 1. Define electrific...

RMI 213 Principles of medical imaging Lecture 5 Electricity and Magnetism Slide 1 fchs.ac.ae Learning Outcomes At the conclusion of this lecture, associated tutorial and practical session (if relevant), you will be able to: 1. Define electrification and provide examples 2. State the laws of electrostatics 3. Identify units of electric current, electric potential, and electric power 4. Identify the interactions between matter and magnetic fields. Slide 2 fchs.ac.ae Prescribed Text Bushong, S.C., Radiologic Science for Technologists, 10th edition, Mosby/Elsevier; St Louis, 2012, pages 60-74. Notes: 1. Each lecture in this course will relate very closely to a specific set of pages in the above text. It is strongly recommended that students read the pages indicated prior to coming to the lecture. 2. The students outcomes listed at the commencement of each lecture are essentially those found in the prescribed text for the relevant chapter. Slide 3 fchs.ac.ae Electrostatics Matter has mass, and an energy equivalence Matter contains charged particles (electrons and protons) Matter itself may be charged Positive – fewer electrons (e) than protons (P) Negative – more electrons than protons The charge on an electron is qe = –1.6  10-19 C The charge on a proton is qp = +1.6  10-19 C Any charge imbalance may be caused by contact, by friction, or by induction Slide 4 fchs.ac.ae Electrostatic Laws Charges are associated with electric fields “E” E is directed radially outwards from a positive charge; E is directed radially in towards a negative charge. Between two (or more) charged particles there is a force “F” Like charges (same sign) repel; Unlike charges (opposite sign) attract. The direction of E for a charged object can be visualized as the direction in which a positive charge would move. The force between two charges, Q1 and Q2 has magnitude F = k(Q1 Q2)/d2 (Coulomb’s law; note it is an inverse square law), where k is a constant and d is the distance between the two charges. Slide 5 fchs.ac.ae Electric Field Distribution Electric field distributions for a number of simple cases are shown; note E directions as indicated by arrows. The repulsion/attraction is clearly seen in the E field distributions in diagrams C, D and E. In case F, the diagram shows that neutral particles such as the neutron (N) produce no electric field. Bushong, Figure 4-6, page 64 Slide 6 fchs.ac.ae Electric Charge Distribution Electric charge distribution in matter is either uniform throughout, or located on the material surface; For a conductor, the electric charge is concentrated on the surfaces with the highest curvature; In most cases of interest here, it is the free electrons that provide the moving charge in an electrical conductor. Bushong, Figures 4-7, 4-8, page 65 Slide 7 fchs.ac.ae Electric Potential To move one charge closer to another charge of the same sign (they repel, remember), you have to do work; Doing work implies increasing the energy of the system (and lowering your total energy); Electric charges have Potential energy, energy by virtue of their position in the fields of other charged particles; e.g. two positively charged bodies will, if released, accelerate away from each other (potential energy → kinetic energy). The electric potential or voltage V is the potential energy per unit charge; units joule per coulomb = volt; 1 V = 1 J/C Don’t confuse V (voltage: italic) with unit V (volt: upright) In UAE, the mains supply is 220 V (AC, expressed as RMS) Slide 8 fchs.ac.ae Electrodynamics Electrodynamics is the study of electric charges in motion, Concerned with electric current in electric conductors. A conductor allows easy flow of charge (electrons, usually); An insulator is material where no current can be established; A semiconductor is a material where, under certain conditions, the movement of charge may be controlled and behavior may vary significantly between conductor-type and insulator-type. At normal temperatures, all materials resist charge flow to some extent (insulators totally, conductors very little). Slide 9 fchs.ac.ae Superconductors Superconductors have zero resistance below their critical temperature TC Superconductors find use in magnetic resonance imaging, MRI Bushong, Figure 4-9, page 67 Slide 10 fchs.ac.ae Material Examples Bushong, Table 4-1, page 67 Slide 11 fchs.ac.ae Electric Circuits Electric circuits are comprised of: conducting wires (assumed to have zero resistance), circuit elements like resistors, capacitors, inductors, diodes, voltage sources: AC and DC (batteries), current sources. Parameters of relevance are the voltage, V , across elements, and the current, I , through elements. Generally in DC circuits, we use upper-case: V, I. In time-varying situations and AC circuits we use lower-case: v, i. Slide 12 fchs.ac.ae Ohm’s Law Ohm’s Law: V = IR (DC cases), or v = iR (AC cases) The ratio of the voltage across the component to the current though the component is a constant; the resistance, R For certain circuits and components, Ohm’s Law holds Worked Example: Q2. A DC voltage of 5.0 V exists across a resistor R = 10 . In a closed circuit where a current can be established, determine the current. We are given voltage V and resistance R and asked to find the current I... Use Ohm’s Law V = I R ; rearrange: I = V / R Substitute: I = 5.0 V / 10  Answer: I = 0.5 A (DC) Slide 13 fchs.ac.ae Circuit Element / Component Symbols ▪ This table shows the symbols for common circuit components. A DC voltage source (a battery) is An AC voltage source is Bushong, Table 4-2, page 66 Slide 14 fchs.ac.ae Series Circuits – Resistors Here components are connected one after the other with wires, and connected to the power supply. The total resistance is the sum of the individual resistances, Bushong, Figure 4-11, page 67 RT = R1 + R2 + … etc. The current through all components is identical, I1 = I2 = … etc. The total voltage is the sum of the voltages, VT = V1 + V2 + etc. The voltage across an individual resistor is VR = IR Slide 15 fchs.ac.ae Parallel Circuits – Resistors Here components are connected between the two power supply wires. The total resistance, RT , is expressed through: 1 1 1 1 = + + +... etc. RT R1 R2 R3 Bushong, Figure 4-12, page 68 The currents through all components sum to the total current; IT = I1 + I2 + … etc. The voltage is the same across all components, and equal to the supply voltage, VT = V1 = V2 = … etc. Slide 16 fchs.ac.ae Simple Circuits – Example Calculations Q3. What is the equivalent resistance of six 10  resistors connected in series? Use formula RT = R1 + R2 + … etc. Substitute: RT = 10  + 10  + 10  + 10  + 10  + 10  Answer: RT = 60  Q4. What is the equivalent resistance of these six 10  resistors connected in parallel? 1 1 1 1 Use formula = + + +... etc. RT R1 R2 R3 1 1 1 1 1 1 1 6 Substitute: = + + + + + = RT 10 10 10 10 10 10 10 Answer: RT = 10/6 = 1.7  Slide 17 fchs.ac.ae Current and Electron Flow “Conventional current” – an historical definition – is the direction in which positive charges would flow. The negatively charged electrons – the actual moving charges in most cases – move in the opposite direction! In a DC circuit, we show the conventional current direction with an arrow. Current is the rate at which (positive) charge moves, I = Q/t So for electrons, I = –Qe/t (as Qe is negative) If an electron goes this way , the current goes this way In the AC case we have i = q t or, more generally, i = dq/dt Slide 18 fchs.ac.ae DC and AC In DC cases, the charge flow is constant in time, I = Q/t = constant; the voltage V is also constant. In AC cases, the current varies; with mains supply, the time variation for both current and voltage is sinusoidal: v = v0 sin(2ft) in the UAE the mains frequency is f = 50 Hz. Bushong, Figures 4-13 & 4-14, pages 68, 69 Slide 19 fchs.ac.ae Electric Power Electric power, P, is measured in watts, W 1 W = 1 J/s 1 W is the equivalent of a 1 A current flowing in a circuit established by a 1 V voltage across the circuit/component In DC cases, this is simply calculated; PDC = I V ( = I2R = V2/R ) Slide 20 fchs.ac.ae Electric Power In AC cases, we first need the average voltage and current: For sinusoids which have positive and negative values, a simple average would yield zero, so Instead, we square each value, then calculate the mean of all of the squares, then take the square root of that mean; the RMS (root-mean-square) value is square root of the mean of the squared quantity. In the UAE the mains voltage is 220 VRMS PDC = IV = I2R = V2/R PAC = iRMSvRMS = iRMS2 R = vRMS2/R Slide 21 fchs.ac.ae Electric Power – Example Calculation Q5. If the cost of electric energy in the UAE is 1 Dhs per kW-hr, what will it cost to operate a 100 W light for an average of 5 hours per day for 30 days? We are given the power rating of the light, the times it is used and the cost per energy unit (kW-hr)... Use formulae Energy used = Power × time, and Cost = (cost per energy unit) × (energy used) Substitute: Energy used = (100 W) × t = (100 W) × (5×30) = 15000 W-hrs = 15 kW-hrs 1 Dhs Substitute: Cost = kW. hr × 15 kW-hrs Answer: Cost = 15 Dhs Slide 22 fchs.ac.ae Magnetism In its simplest form, a magnetic field is associated with a moving electric charge; Thus an electron in orbit around the nucleus in an atom produces a magnetic field. For an atom we define the strength of the atomic magnetism by the magnetic moment, m. Bushong, Figures 4-15 & 4-16, page 71 Slide 23 fchs.ac.ae Moving Charged Particles A spinning charged particle will also produce a magnetic field; This gives rise to the quantum attribute of fundamental particles called ‘spin’. Strangely, neutrons also possess this quantum attribute, even though they are, overall, electrically neutral particles. Bushong, Figure 4-17, page 71 Slide 24 fchs.ac.ae Bar Magnets A bar magnet is a macroscopic piece of material made up of N atoms, each carrying a permanent magnetic moment, m, so M = Nm The magnetic moment is a ‘dipole’ (a ‘bar magnet’ at the atomic or molecular level) Permanently aligned dipoles are referred to as ferromagnetic materials, and have a N and S pole. Bushong, Figure 4-18, page 71 Slide 25 fchs.ac.ae Magnetic Materials Magnetic materials are classified by their interaction with an external magnetic field, H. Diamagnetic – very weak (effectively zero) interaction with H Paramagnetic – weak interaction with H Ferromagnetic – strong interaction with H Bushong, Table 4-3, page 73 Slide 26 fchs.ac.ae Electromagnets A current in a coil of wire (moving charges, remember) can act very much like a bar magnet. The current direction at each end of the coil defines the magnetic pole. I, current I, current S N Bushong, Figure 4-20, page 72 Slide 27 fchs.ac.ae Electromagnetism A moving charge constitutes a current A current produces a magnetic field A coil of wire is referred to as a solenoid A solenoid with a DC current, I, produces a magnetic field, H, that is proportional to the current; H  I H is (approximately) constant within the solenoid, and (approximately) zero outside the solenoid The magnetic field H has units of amp/m, A.m-1 A solenoid with an AC sinusoidal current, i = i0 sin(2f t), produces a magnetic field inside the solenoid; H = H0 sin(2f t) Slide 28 fchs.ac.ae  Electromagnets Arranging wire in a coil and running a current through produces a magnetic field that looks a lot like a bar magnet called an electromagnet putting a real magnet inside, can shove the magnet back and forth depending on current direction: called a solenoid fchs.ac.ae 29 Summary Check that you can satisfy the learning outcomes for this lecture Go over calculations/exercises undertaken during the lecture Make sure you can define the following terms: electric charge, electric field and its distribution electrostatics law: force between charges Ohm’s law, voltage, current and resistance series and parallel circuits electric power and use of RMS in AC circuits relation between moving charge and magnetic moment magnetic poles for current carrying coils (solenoids) Slide 30 fchs.ac.ae