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Magnetism Magnets You have likely played with magnets in the past. But probably not very formally. Magnets are interesting Origin: β’ Magnetite is a naturally occurring magnetic mineral β’ First record of discovery of properties from 2600 years ago β’ Named after region where it was discovered: the Greek island of Magnesia Magnets are interesting Properties: Magnets exert force on other magnets from a distance: 1 πΉππππππ‘ππ β πππ π‘ππππ 2 ~ Coulombβs Law, but for magnets The connection is closer than you think! Thanks, Einstein (and Derek Muller for explaining it so lucidly) Magnets are interesting Properties: All magnets have north and south pole: likes repel; opposites attract If you were to split a magnet in two, you would end with two magnets, each with a north and south pole. True even to the atomic level! Magnetic field The force exerted on other objects can be described with a βmagnetic fieldβ. β’ Like the electric field, imaginary but useful for describing interactions Magnetic field Conventions β’ Points away from north pole, towards south pole β’ Lines never cross β’ Tighter lines = more intense field β’ βFluxβ, ο Greek letter phi β’ Pronounced βfeeβ β’ Measures magnetic field strength per area Magnets and currents Magnetism is connected to electricity β’ In 1820, Danish scientist Hans Christian Oersted noticed deflection of compass needle in presence of electric current. β’ Laid the foundation for Henry, Faraday, Maxwell, Tesla, and Einstein. A long wire carrying current creates a circular magnetic field A loop of wire carrying current creates a linear magnetic field See more: Magnetic Field Demonstrations Simple Wire Coils Right-hand rule #1 1. Point your thumb in the direction of the flow of current 1. by convention, from positive terminal to negative terminal 2. Imagine curling the fingers of your right-hand around the wire. 3. The circular magnetic field around a long current-carrying wire goes in the same direction as your fingers. Magnetic forces on moving charged particles Positively charged particles move into page. Passing through a magnetic field goes from north to south (here: right to left) Moving particles experience upward force. Magnetic forces on moving charged particles Positively charged particles move into page. Passing through a magnetic field goes from north to south (here: left to right) Moving particles experience downward force. Magnetic forces on moving charged particles Positively charged particles come out of the page. Passing through a magnetic field goes from north to south (here: right to left) Moving particles experience downward force. Right-hand rule #2 1. Point your right forefinger in the same direction as the movement of charge. 2. Point your middle finger in direction of magnetic field. 3. Your thumb points in the direction of the force POSITIVELY-charged moving particles will experience. In real lifeβ¦ Walter Lewin ~10:00 β 11:50 Try it! Positively charged particle come out of page Passing through a magnetic field goes from north to south (here: left to right) In what direction will the particles feel a force? Try it Negatively charged particles move into page. Passing through a magnetic field goes from north to south (here: right to left) In what direction will the particles feel a force? Think about itβ¦ Is this drawing accurate? Applications Televisions and mass spectrometers use precisely this physical principal to work. Mathematical model Increase current ο° increase force ο±I ο°ο± F Increase length of wire exposed to field ο° increase force ο±π ο°ο± F Increase strength of magnetic field ο° increase force ο±B ο°ο± F F = I π B sinΞΈ Mathematical model Force is greatest when ο ο± = 90ο°. Current running perpendicular to magnetic field experiences force. Force is zero when ο± = 0ο° Current running parallel to magnetic field experiences no force. F = I π B sinΞΈ Quantifying magnetic field strength πΉπππ₯ = I π B so, π΅ = πΉπππ₯ πΌπ 1.000 tesla is defined as the strength of the magnetic field that will exert 1.000 N of force on 1.000 m of wire carrying 1.000 A. ππππππ πππππ = ππππππ πππππ π΅ π»= π¨π How big is a tesla? Factor Example 10-12 Primatesβ brains 10-9 Magnetic strength of heliosphere 10-6 Strength of magnetic tape near tape head 10-5 Strength of Earthβs magnetic field 31 οT near equator; 58 οT @ 50ο° 10-3 Strength of typical refrigerator magnet 100 Typical coil gap of typical loudspeaker Strength of coin-sized neodymium magnet 101 Strength used to levitate frog 102 Strongest pulsed magnet produced in lab 106 Strength of neutron star Example A loop of wire (30 cm long and 10 cm wide) is partially suspended in a magnetic field and hangs from a scale that reads zero when the current is zero. If the scale reads 3.48 x 10-2 N when current of 0.245 A passes through the wires, calculate the strength of the magnetic field. The magnetic field points into the page. Solution Use the right-hand rule to compare the direction of the force on the downward portion of the loop with the direction of the force on upward portion of the loop. Use the right-hand rule to determine the direction of the force experienced by the bottom portion of the loop. Example Try it first. Then delete this box. F = I π B sinΞΈ So B = F Try it first. Then delete this box. I π sinΞΈ 3.45 x 10β2 π Try it first. Then delete this box. B= (02.45 A)(0.1 m)(sin 90°) N Try it first. Then delete this box. B = 1.42 = 1.42 T Am This process is used to precisely calculate the strength of electric fields. Solution What would the force on the coil be if it were entirely inside the magnetic field? Mathematical model v2 πΉπππ₯ = I π B where I = Nq/t l = vt So, πΉπππ₯ = NqvB So, the force on each particle, πΉπππ₯ = qvB or πΉ = qvB sinΞΈ Example A negative charge βQ is placed at rest near a magnet. In what direction will it move? In what direction would a positively charged particle +Q move? @ v = 0 m/s, F = 0 N It wonβt move at all! Try it first. Then delete this box. Example A proton moving vertically upward at a speed of 5.0 x 106 m/s passes through a magnetic field. When it passes through the field, it experiences a 8.0 x 10-14 N push to the west. If a northward-moving proton experiences 0 N, a) In what direction is the magnetic field in this area? b) How strong is the field in this area? Solution - a A proton moving vertically upward passes through a magnetic field. When it passes through the field, it experiences a push to the west. A magnetic field exerts a force towards the west on a proton moving vertically upward If a northward-moving proton experiences 0 N, in what direction is the magnetic field in this area? Experiences force to the west By right-hand rule, upward traveling positive charge Try it first. westward Then delete thisforce box. experiencing must be traveling through field pointing north. Solution - b A proton moving at a speed of 5.0 x 106 m/s experiences a 8.0 x 10-14 N push to the west. How strong is the field in this area? πΉ= F it first. Thenso, deleteπ΅ this= box. qvB Try sinΞΈ q v sinΞΈ β14 π΅= 8.0 x 10 N Try it first. Then delete this box. 1.6 x 10β19 C 5.0 x m 6 10 s B=0.10 TTry it first. Then delete this box. (sin90°) This process is used to precisely calculate the charge and mass of particles. Thereβs more! β’ Walter Lewin