Lecture 13: Magnetic Sensors & Actuators

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1 MECH 466 Microelectromechanical Systems University of Victoria Dept. of Mechanical Engineering Lecture 13: Magnetic Sensors & Actuators 1 Magnetic Fields Magnetic Dipoles Magnetization Hysteresis Curve Lorentz Force Current Carrying Wires Overview 2

2 Magnetic Sensing and Actuation Magnetic fields and forces can be used to actuate micro-scale devices, or be used to create novel micro-sensors. Applications include: Micro-Sensors (Resonant magnetometer with CMOS) [B. Eyer, K. Pister, et al] Micro-Inductors and Microcoils [N. Dechev] Self-Assembly of Microstructures [C. Liu, J. E. Schutt-Aine] 3 Review: Basics of Magnetism Magnetic fields can arise in two main ways: (A) Motion of Charge Magnetic Field around a moving Positive Charged Particle [MIT TEAL/Studio Physics Project] (B) Magnetic Materials Magnetic Field around a Bar Magnet [Wikipedia] 4

3 Magnetism Due to Moving Charge A current-carrying conductor such as a wire, will induce a magnetic field around it, as follows: H Current Flow i H Front View (Current moving Out of Page ) Where: H is the magnetic field intensity. Note: You can use the right hand rule to determine the orientation of the magnetic field around the conductor. (Right Hand Rule: Imagine grasping the wire conductor, with your thumb pointing in the direction of the current, and note that your fingers curl in the direction of the magnetic field.) 5 Magnetism Due to Magnetic Materials Magnetic fields also arise in permanent ferromagnets, also known as hard magnets. Any piece of magnetic material is comprised of many magnetic dipoles : For magnetic materials in a natural or raw state, these magnetic dipoles may be unaligned: - Therefore, there is little or no net magnetic field Image of un-aligned magnetic dipoles within a material. 6

4 Magnetism Due to Magnetic Materials Creation of permanent magnets: (1) An appropriate hard-magnetic material is elevated to a high temperature, and subjected to a very strong external magnetic field. (2) Due to the elevated temperature, the magnetic dipoles move easily, and align approximately with the magnetic field. (3) The temperature is then reduced, and the magnetic dipoles become frozen in their aligned positions. The external magnetic field is removed, leaving the magnetized material. (4) The dipoles remain aligned to a high degree at all times, thereby creating a permanent magnetic field. In soft magnets the dipoles are normally un-aligned, and must be driven into alignment by an external magnetic field H, to induce a further magnetic field by the soft magnet. 7 Magnetism Due to Magnetic Materials The magnetic field density, B, inside a piece of magnetic material is measured in units of: The magnetic field density is also known as the magnetic induction or the magnetic flux density. 8

5 Difference Between B and H Fields H is defined as the magnetic field intensity and describes a magnetic field in space, which is measured in units of: A good analogy to H, is the electric field E. The relationship between B and H is presented as: 9 Difference Between B and H Fields Lets define B more generally as: the magnetic field density within any material or within any medium. In this sense, either B or H can be used to describe any magnetic field. ** Even if the B field is in air, or in empty space.** Where as B is related to the medium properties, while H is not. 10

6 Magnetization Hysteresis Curve B saturation ramanent magnetization initial magnetization The area of the hysteresis loop is related to energy dissipation upon reversal of field Hc Hc H coercivity (field necessary to cancel internal magnetization) Fig. 8.1 Magnetization Hysteresis Curve [C. Liu] 11 Magnetization Hysteresis Curve 1.2 T B saturation Hc H (1000 A/m) Fig. 8.2 Magnetization Hysteresis Curve [C. Liu] 12

7 Example Using: Magnetization Hysteresis Curve See Class Notes 13 Lorentz Force The Lorentz Force arises as a charged body moves through a magnetic field, and is governed by: Where: F - Force Matrix q - total charge of body v - Velocity Matrix of body B - Magnetic Field Matrix This equation can be simplified for a one-dimensional case, as: Where: F - Force q - total charge of body v - Velocity of body B - Magnetic Field θ- Angle between B Field and v 14

8 Lorentz Force on a Current-Carrying Wire The Lorentz Force acts on a stationary wire that carries current, while that wire is in a magnetic field. Think of the current as the moving charge. Therefore, the force can be derived as: conducting wire I Where: i - Current in wire L - Length of wire B Lorentz force - Note, the derivation was done using the expression qv = il where: q - Total charge v - Velocity [Fig. 8.3 from Foundations of MEMS, Chang Liu] 15 Example: Lorentz Force on a Current-Carrying Wire See Class Notes 16

9 Electromagnetic Induction When a conductor is moved through a magnetic field, a current will arise (will be induced) in the conductor. This is the principle of electromagnetic induction, and is described by Faraday s Law: Where: E - Electric Field dl - an infinitesimal element of the contour C B - Magnetic Field Density da - an infinitesimal area of the surface S where contour C and surface S are related by the right hand rule This general equation can be simplified to: Where: emf - Electromotive Force (in units of Volts) A - Area through which magnetic flux passes ϕ - angle between a vector perpendicular to the area A, and the magnetic field direction 17 Electromagnetic Induction In the case of a conductor (such as a wire), that is forced to move through a magnetic field, we can re-write the equation as: Conductor, Length L Where: emf - Voltage across Conductor L - Length of the Conductor v - Velocity of the Conductor where B and v are related by the right hand rule Conductor Velocity v B Field To find the current, i, that is induced in the conductor, we need to know the resistance, R, of the conductor, and can write the expression: 18

10 Electromagnetic Induction Forces When the conductor is moved through the magnetic field, a force will arise to maintain the conservation of energy Lenz s Law. When the conductor is moved with a velocity v as shown, a current will be induced. Due to this current, a Lorentz force FL will arise as shown in the diagram, in red. Therefore, a force F will arise to counteract this force, as described by: Current i Force F Conductor Velocity v Lorentz Force FL Where: it is assumed that B and v are at 90 degrees B Field 19 Electromagnetic Induction in a Loop There are three ways an emf can be induced in a loop: - Changing the magnetic field - Changing the area of the loop - Changing the angle between the field and the loop emf in loop will only occur during a change of one of these three values! i.e. no change = 0 emf Current i Recall: B Field 20

11 Example #1: Induction in a Microcoil A diagram shows a 3 loop microcoil. The dimensions of the loops are 50 um by 40 um. If the B field is changing from 0 Tesla to 1 Tesla in 10 microseconds, find the emf across the leads. Assuming a linear change with time for B: emf Therefore: B Field 21 Magnetic Dipoles in Magnetic Fields The operation of a compass is well known. The needle, which can be considered as a magnetic dipole, is held in an almost frictionless way. When the needle starts at some arbitrary position, a magnetic torque will be developed, such that the needle will align itself with the Earth s magnetic field. [Fig. 8.4 from Foundations of MEMS, Chang Liu] 22

12 Magnetic Dipoles in Magnetic Fields External magnetic fields can be classified into two main categories: - Uniform magnetic fields - Non-uniform magnetic fields The effect of these fields on permanent hard magnets is intuitive, in that they behave much the same way as a compass needle. The effect of these fields on soft magnetic materials, is interesting, in that these materials often exhibit shape anisotropy. This means that soft magnetic materials, when subjected to a magnetic field, will tend to develop a magnetic moment M, based on their shape, rather than the orientation of the field. Practically, soft magnets will develop a moment M, on their longitudinal axis, irrespective of of the direction of the induction field. 23 Magnetic Dipoles in Magnetic Fields Consider the diagram below: permanent magnet soft magnet (a) No external magnetic field (b) Uniform external magnetic field [Fig. 8.5 from Foundations of MEMS, Chang Liu] 24

13 Magnetic Dipoles in Magnetic Fields Consider the diagram below: H 1 H 2 (c) Non-uniform external magnetic field [Fig. 8.5 from Foundations of MEMS, Chang Liu] 25

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