RMI 213 Principles of Medical Imaging Lecture 6 PDF

RMI 213 Principles of medical imaging Lecture 6 Electromagnetic Induction Slide 1 fchs.ac.ae  https://youtu.be/CWulQ1ZSE3c?t=41 Learning Outcomes At the conclusion of this lecture, associated tutorial and practical session (i...

RMI 213 Principles of medical imaging Lecture 6 Electromagnetic Induction Slide 1 fchs.ac.ae  https://youtu.be/CWulQ1ZSE3c?t=41 Learning Outcomes At the conclusion of this lecture, associated tutorial and practical session (if relevant), you will be able to: List the magnetic parameters and explain their origin State the relation between B, H and M Define the constant 0 Explain what is meant by magnetic susceptibility State Lenz’s law and use this in simple calculations Describe in general terms how an electric motor works Describe in general terms how an electric generator works Explain the operation of a transformer Slide 2 fchs.ac.ae Prescribed Text Bushong, S.C., Radiologic Science for Technologists, 10th edition, Mosby/Elsevier; St Louis, 2012, pages 75-83. On-line movie clips of the workings of motors and generators at http://www.animations.physics.unsw.edu.au/jw/electricmotors.html 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 Laws of Magnetism There is no ‘free’ pole (like a free charge) All magnetic entities have both a N and S pole A magnetic arrangement of a N and a S separated by a small distance is called a magnetic dipole (like a bar magnet) Otherwise, the laws of magnetism are similar to those for electrostatics Like poles (N-N, S-S) repel; Unlike poles (N-S) attract; Slide 4 fchs.ac.ae Magnetic Force A current-carrying conductor generates a magnetic field; A current-carrying conductor placed in a magnetic field experiences a force; think of this as two magnetic fields interacting. The magnitude of the force is F = IB sin() where: I is the electric current,  is the length of the conductor, B is the magnetic field of induction, and  is the angle between the direction of current flow and B (maximum F when  = 90) The direction of the force is perpendicular to both I and B http://commons.wikimedia.org/wiki/File:Right_hand_rule_cross_product.svg Slide 5 fchs.ac.ae Straight Current-Carrying Wire A current produces a magnetic field, H Lines of a magnetic field are always closed loop The magnetic field strength is H = I/(2R), units of Amp/m (A.m-1 ) The Right-Hand (RH) rule: With your thumb in the direction of the current, your fingers will curl around in the direction of H. Bushong, Figure 4-29, page 76 and http://people.stfx.ca/jpowell/work/lab/rightframe.html Slide 6 fchs.ac.ae Magnetic Susceptibility Magnetic permeability Ability of a material to attract the lines of magnetic field intensity, given by  r The magnetization “M” of a material is shape dependent The susceptibility of a material to be magnetized when placed in a magnetic field H is given by M = H ( = Greek letter “chi”) where  = (r – 1) is called the magnetic susceptibility “Degree to which a material can be magnetized” Slide 7 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 8 fchs.ac.ae Magnetic Materials Magnetic materials are characterized by their value of r State r Material Non Magnetic 1 Air,wood,glass Diamagnetic  1 – 10-3 Copper Paramagnetic  1(but Gadolinium small) Ferromagnetic >> 1 (up Iron,Nickel,Cobalt to 1000) Slide 9 fchs.ac.ae Electromagnetism Any change in motion induces a magnetic field A coil of wire is called a solenoid, H = nI N S The solenoid acts like a bar magnet; In the solenoid, the direction of H is given by the right-hand (RH) rule: with your thumb in the direction of current at each point, your fingers will point along H. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html Slide 10 fchs.ac.ae Electromagnetic Flux Consider a loop of wire of area A placed in a B-field Magnetic flux Φ through a surface is the component of the magnetic B field passing through that surface B  Magnetic flux, , passing through this loop area is A defined by  = BA cos() B B – magnetic field A- Area A - angle http://simple.wikipedia.org/wiki/Magnetic_flux Slide 11 fchs.ac.ae Slide 12 fchs.ac.ae Electromagnet An electromagnet is a current carrying coil of wire wrapped around an iron core, which intensifies the induced magnetic field. H depends on the number of turns of wire per unit length “N/” H = (N/)I = nI , with n = N/ Magnetic field of induction “B” is given by B = 0 r H Unit of B is Tesla where 0 is the magnetic permeability of a vacuum, r is the relative permeability of the material placed in the field H Magnetic permeability of a vacuum is 0 = 4  10-7 (SI units) r is a dimensionless number (large for ferromagnets) Slide 13 fchs.ac.ae Electromagnet – Example Calculation Q1. A coil has 1000 turns and is 50 cm long. With a DC current of 200 mA through the windings, what is the field inside the coil? Slide 14 fchs.ac.ae Electromagnetic Induction - Faraday’s law An electric current is induced in a circuit if some part of that circuit is in a changing magnetic field. “Varying magnetic field intensity induces an electric current” Magnitude of induced current depends on: 1. Strength of magnetic field 2. Velocity of magnetic field as it moves past the conductor 3. Angle of the conductor to the magnetic field 4. Number of turns in the conductor. Slide 15 fchs.ac.ae Electromagnetic Induction Lenz’s law predicts an output voltage across the coil when any of the following occurs: A change in B Moving a magnet towards or away from a stationary coil (as shown opposite) A change in A Changing the coil dimensions (not common) A change in  Changing the angle between B and coil area Bushong, Figure 4-33, page 77 Slide 16 fchs.ac.ae Lenz’s Law Across the ends of a loop of wire in a B-field you will measure a voltage proportional to the time rate change of flux though the coil. This is expressed by Lenz’s Law: V = –[BA cos()]/t V – Voltage, B – Magnetic filed, A-Area , - angle, t- time interval The induced voltage is in such a direction that, if the loop was closed and a current was developed, it would produce a magnetic field to oppose the flux change; that is the meaning of the –ve sign at the start of Lenz’s Law. https://www.youtube.com/watch?v=wZ0YD451S-Y Slide 17 fchs.ac.ae Electromagnetic Induction – Example Calculation Q2. A square coil of side length 5 cm, with 100 turns of wire, sits with the plane of the coil perpendicular to a B field of 0.04 T. The coil is rotated 90 degrees in 0.1 s. What is the average voltage across the coil during this time interval? Slide 18 fchs.ac.ae Electric Motor In an electric motor an electric current produces a mechanical motion (motion of compass needle) The simplest arrangement is to have a coil of wire, carrying a constant, DC, current, between poles of a magnet This produces a force on one side of the coil, as shown. An equal and opposite force exists on the other side of the coil. Together, the forces produce a turning force, a torque that spins the coil. The current direction is reversed using a split (or commutator) ring. http://www.animations.physics.unsw.edu.au/jw/electricmotors.html Slide 19 fchs.ac.ae Electric Generator An electric generator is a device that converts mechanical energy to electrical energy. A generator forces electric current to flow through an external circuit Inductor An inductor is a coil of wire wound around a former, with N turns over a length of  m, with n = N/ The former is usually a ferrite material with large r Slide 20 fchs.ac.ae Transformer If we form two inductors around the same magnetic former, we have a transformer. This is used to change the magnitude of Magnetic former an input sinusoidal voltage vin The flux is proportional to NP , the number of winding on the input, or vin = vP vout = vS primary “P” side of the transformer. The output voltage is proportional to the number if windings NS on the output, or secondary “S” side of the transformer: NP coils NS coils vout/vin = vS/vP= NS/NP Bushong, Figure 4-36, page 79 Slide 21 fchs.ac.ae Transformer – Example Calculation Q3. For an ideal (100% efficient) transformer, the input side has 100 turns and the output side has 2000 turns. (a) What is the turns ratio? (b) If the input voltage is sinusoidal with an RMS value of 10 V, what is the output voltage? Slide 22 fchs.ac.ae 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: magnetic field strength, magnetic field of induction magnetic material magnetic flux electromagnetic induction inductor Use Lenz’s law in simple calculations Use the transformer equation in simple calculations Slide 23 fchs.ac.ae