SOLENOIDS Ryan Rhoades PHY3091: Communication in Physics 3/3/2014 via http://members.wolfram.com/jeffb/visualization/solenoid.jpg INTRODUCTION Basics of electromagnets and solenoids Electromagnetic principles of the solenoid Applications and wide-ranging use ELECTROMAGNET HISTORY By the 1800’s electrical theory was just in its infancy In 1819, Hans Christian Ørsted discovered that electricity can produce a magnetic field- magnetic induction In 1820, André Marie Ampère theorized the helical solenoidal coil as an effective way to produce magnetic fields Lead to the development of the electromagnet in 1824 by William Sturgeon via Wikimedia Commons- http://en.wikipedia.org/ wiki/File:Sturgeon_electromagnet.png ELECTROMAGNETS AND SOLENOIDS Electromagnets depend on this solenoidal coil to magnetize a ferromagnetic material. The solenoid coil: converts the applied electric current to a harnessable magnetic field produces a near-uniform magnetic field that propagates within the core in order to create a magnet via Education.com- http://01.edu-cdn.com/files/static/mcgrawhillimages/9780071382014/f0355-01.jpg ELECTROMAGNETS AND SOLENOIDS Electromagnets depend on this solenoidal coil to magnetize a ferromagnetic material. The solenoid coil: converts the applied electric current to a harnessable magnetic field produces a near-uniform magnetic field that propagates within the core in order to create a magnet via Wikimedia Commons- http://en.wikipedia.org/wiki/ File:Electromagnet_with_gap.svg A SUMMERY OF THE MAGNETIC FIELD- WIRE A force was observed in wires carrying current (I) through a magnetic field. Magnetic force: ! ! ! ! ! FB =qv ⇥ B =IL ⇥ B The field (B) that resulted in this force was then derived in the integrated Biot-Savart law: ! µ0 B = I 4⇡ I ! d L ⇥ r̂ r2 via Wikimedia Commons- http://en.wikipedia.org/wiki/ File:Electromagnetism.svg A SUMMERY OF THE MAGNETIC FIELD- WIRE This defined magnetic induction (B) yields a magnitude azimuthal to a straight long wire at a distance (r) away µ0 I B= 2⇡r Now, if one were to take the circular line integral of the field at that distance (r) around the wire, I ! ! µ0 I B ·dr = 2⇡r = µ0 I 2⇡r via Wikimedia Commons- http://en.wikipedia.org/wiki/ File:Electromagnetism.svg AMPERE’S LAW I ! ! B · d r = µ0 Ie This relation, Ampère’s circuital law, holds generally, and that if one can create an encircling loop of a charge carrier, then the result will always hold. B-FIELD IN A COILED WIRE (SOLENOID) For an ideal, infinitely long solenoid, we still can apply Ampère’s law. Outside of the solenoid, the only dependence of the B-field is azimuthal around the solenoid I ! ! B · d r = B 2⇡⇢ = µ0 I via HyperPhysics- http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/ imgmag/sol.gif µ0 I )B = 2⇡⇢ B-FIELD IN A COILED WIRE (SOLENOID) Inside, if once considers the given Ampère loop, the component dependence is a longitudinal one I ! ! B · d r = Bz L = µ0 N I ! via HyperPhysics- http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/ imgmag/sol.gif N ) Bz = µ0 I L Due to the nature of the azimuthal B-field of a wire, tightly spaced coils create a near-uniform field directed in one direction in the interior of the solenoid cavity, independent of radial distance. IDEAL VS. REAL SOLENOID Even though the B-field expression of the interior solenoid field is for an ideal infinite solenoid, this approximation for a finite solenoid The azimuthal and non-zero outside longitudinal B-field components will be much smaller that the near-uniform field inside The straight finite solenoid can be seen as an analog to a bar magnet with comparable magnetic field lines IDEAL VS. REAL SOLENOID via HyperPhysics- http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/ imgmag/barsol.gif SELF-INDUCTANCE OF A SOLENOID Solenoids also have the property of self-inductance and behave as an inductor Self-inductance (L) occurs when a circuit’s own induced magnetic field opposes changes in the current, inducing an opposing electromotive force (emf) Self-Inductance is defined via the magnetic flux of an inductor, as L= B I Therefore, for a solenoid of N-turns the self-inductance will be approximately L= B I = N N µ0 I L A I N2 2 = µ0 ⇡r L TAILORING A SOLENOID One can change the electrical and shape parameters of the solenoid, but one can also change the solenoid cavity For electromagnets, a ferromagnetic core is placed in the solenoid to direct the magnetic field. This changes the field in the solenoid via a new effective permeability constant N B = µ0 I L N ) B = µe↵ µ0 I L where 1 µe↵ 0 SOLENOID APPLICATIONS The Compact Muon Solenoid @ CERN Magnetic Resonance Imaging (MRI) Cars Toroids COMPACT MUON SOLENOID The CMS is a particle detector experiment at the CERN Large Hadron Collider. The experiment’s solenoid is comprised of superconducting coils cooled to -268.5℃ able to generate B-fields of near 4 T (with inductance values of 14H and operating currents of 19,500A) with a diameter of 15m. via CERN- http://cms.web.cern.ch/sites/cms.web.cern.ch/files/styles/ large/public/field/image/0611042_01-A4-at-140001.jpg? itok=jNpvZNf_ The magnet is used to bend the paths of charged particles traveling through a Bfield, allowing them to be traced and detected. COMPACT MUON SOLENOID MAGNETIC RESONANCE IMAGING MRI’s essentially use a oscillating resonant magnetic field in order to align the magnetic moments of water in the body, and excite the hydrogen in the water and detect body tissue based on the relation of the excited particles The solenoid magnets in MRI’s range from 1.5-3T, and now generally made from superconducting coils via Wikimedia Commons- http://en.wikipedia.org/wiki/ File:Mri_scanner_schematic_labelled.svg Requires magnetic gradients MAGNETIC RESONANCE IMAGING CAR STARTER MOTORS A solenoid is present in the starter motors of modern automobile When the ignition switch is turned on, a small current passes through the solenoid. The magnetic field it generates causes the large current contacts for the car battery to close, starting the starter motor via Wikimedia Commons- http://en.wikipedia.org/wiki/ File:Automobile_starter.JPG When the engine starts, the solenoid becomes de-energized, and the starting motor contacts are disconnected from the starting battery TOROIDS A toroid is a solenoid that has its ends fixed to itself Has the property of having a completely confined magnetic field within its interior N B = µ0 I 2⇡r µ0 N 2 r 2 L= 2R via HyperPhysics- http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/ toroid.html This results in higher inductance for electrical components and low electromagnetic interference to circuits CONCLUSION Solenoids are fundamental to electromagnetics Due to their symmetry, they produce near-uniform magnetic fields independent of cross sectional area with little external fields Have wide-ranging applications due to their tunable parameters and properties in generating B-fields REFERENCES CERN, "What is CMS?" 2014 (Feb 28), (2014). HyperPhysics, "http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html," 2014 (Feb, 2014), . John D. Kraus, Electromagnetics, 4th ed. (McGraw-Hill, New York, 1992), . Pual Lorrain and Dale R. Coroson, Electromagnetism: Principles and Applications, 2nd ed. (W.H. Freeman and Company, San Francisco, 1978), . Wikipedia, "http://en.wikipedia.org/wiki/Physics_of_magnetic_resonance_imaging," 2014 (Feb, 28), (2014). Wikipedia, "http://en.wikipedia.org/wiki/Starter_solenoid," 2014 (Feb, 28), (2014). Richard Wolfson, Essential University Physics, 1st ed. (Pearson Addison-Wesley, San Francisco, 2007) Vol. 2.