* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 33. The Magnetic Field
Magnetic stripe card wikipedia , lookup
Electromagnetism wikipedia , lookup
Mathematical descriptions of the electromagnetic field wikipedia , lookup
Neutron magnetic moment wikipedia , lookup
Giant magnetoresistance wikipedia , lookup
Magnetometer wikipedia , lookup
Superconducting magnet wikipedia , lookup
Magnetic monopole wikipedia , lookup
Magnetotactic bacteria wikipedia , lookup
Earth's magnetic field wikipedia , lookup
Lorentz force wikipedia , lookup
Electromagnetic field wikipedia , lookup
Multiferroics wikipedia , lookup
Magnetotellurics wikipedia , lookup
Magnetoreception wikipedia , lookup
Magnetohydrodynamics wikipedia , lookup
Electromagnet wikipedia , lookup
Magnetochemistry wikipedia , lookup
Force between magnets wikipedia , lookup
Chapter 33. The Magnetic Field Digital information is stored on a hard disk as microscopic patches of magnetism. Just what is magnetism? How are magnetic fields created? What are their properties? These are the questions we will address. Chapter Goal: To learn how to calculate and use the magnetic field. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What is the shape of the trajectory that a charged particle follows in a uniform magnetic field? A. Helix B. Parabola C. Circle D. Ellipse E. Hyperbola Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What is the shape of the trajectory that a charged particle follows in a uniform magnetic field? A. Helix B. Parabola C. Circle D. Ellipse E. Hyperbola Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The magnetic field of a straight, current-carrying wire is A. parallel to the wire. B. inside the wire. C. perpendicular to the wire. D. around the wire. E. zero. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The magnetic field of a straight, current-carrying wire is A. parallel to the wire. B. inside the wire. C. perpendicular to the wire. D. around the wire. E. zero. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Earth and Sun are magnetic http://solar.gmu.edu/teaching/2008_CSI769/solar_magnetic_field.jpg Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Connections to current A magnetic field can be sensed with a magnetic material (compass) and is associated with a current. The earth’s field results from large scale internal currents. The field of a permanent magnet results from atomic scale currents. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The field appears only if there is current. It is associated with moving charge. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Source of the Magnetic Field: Moving Charges The magnetic field of a charged particle q moving with velocity v is given by the Biot-Savart law: where r is the distance from the charge and θ is the angle between v and r. (Valid if v<<c.) The Biot-Savart law can be written in terms of the cross product as Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The field of an element of circuit The average B field dB due to the moving charge in an element of circuit of vector length ds carrying current I follows from superposing the fields of the moving charges: dB r dI=Ids µo Ids × rˆ dB = 2 4π r Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The field of straight wire All current elements produce B out of page µ dB = o 4π µ = o 4π µ = o 4π Ids × rˆ r2 I sin θ 2 r I a µo a = I r 2 r 4π ( x 2 + a2 )3 / 2 Add them all up: µo Ia ∞ dx µo I B= = ∫ 4 π −∞ ( x 2 + a 2 ) 3 / 2 2πa r a r = x 2 + a2 x Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 11 EXAMPLE 33.4 The magnetic field strength near a heater wire Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 33.4 The magnetic field strength near a heater wire Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Twice B(Earth). Magnetic field lines Magnetic field lines close upon themselves – they circulate rather them emanate from charges. Although a current loop can appear like a dipole pair of charges, there is no magnetic charge. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Magnetic Dipoles The magnetic dipole moment of a current loop enclosing an area A is defined as The SI units of the magnetic dipole moment are A m2. The on-axis field of a magnetic dipole is Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 33.7 The field of a magnetic dipole Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 33.7 The field of a magnetic dipole Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Magnetic materials The superposition of the fields of a stack of loops is a field like that of a bar magnet. The bar magnetic field results from alignment of many atomic scale electronic currents/ magnetic dipoles. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Line integrals Magnetic field lines close upon themselves – they circulate rather them emanate from poles. The line integral of B around a closed loop is a measure of the strength in circulation. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Ampère’s law Whenever total current Ithrough passes through an area bounded by a closed curve, the line integral of the magnetic field around the curve is given by Ampère’s law: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Ampère’s law example • Could have used Ampere’s law to calculate B µo I ∫ B • ds = ∫ Bds = B ∫ ds = B2π r = µoI ⇒ B = 2π r B||ds path length = 2πr B constant on path Circular path r B(r) Surface bounded by path Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. I The strength of the uniform magnetic field inside a solenoid is where n = N/l is the number of turns per unit length. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Gauss’s law for magnetism • Net magnetic flux through any closed surface is always zero ∫ B • dA = 0 Compare to Gauss’ law for electric field ∫ Qenclosed E • dA = εo No magnetic ‘charge’, so right-hand side=0 in the case of magnet field. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General laws of electromagnetism Gauss’ law Magnetostatics Electrostatics Ampere’s law ∫ B • dA = 0 ∫ B • ds = µ I Qenclosed ∫ E • dA = ε o ∫ E • ds = 0? • Integral of E-field around closed loop is is the change in electric potential going around = zero. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. o x The Magnetic Force on a Moving Charge The magnetic force on a charge q as it moves through a magnetic field B with velocity v is where α is the angle between v and B. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Motion in a uniform constant magnetic field The magnetic force on a moving charge q is perpendicular to B and to v and results in helical motion. (Circular motion if there is no velocity component along the field.) Beam of electrons moving in a circle. Lighting is caused by excitation of atoms of gas in a bulb. http://en.wikipedia.org/ wiki/Magnetic_field Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Derive force by adding forces on charges constituting the current. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Magnetic Forces on Current-Carrying Wires Consider a segment of wire of length l carrying current I in the direction of the vector l. The wire exists in a constant magnetic field B. The magnetic force on the wire is where α is the angle between the direction of the current and the magnetic field. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 33.13 Magnetic Levitation Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 33.13 Magnetic Levitation Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 33.13 Magnetic Levitation Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Interaction between a field and a dipole An current loop in a magnetic field is subject to a net torque aligning the dipole moment with the field. F I τ =r×F ⎞ ⎛ τ = 2⎜ F sin θ ⎟ ⎝2 ⎠ F = IB ⇒ τ = AIBsin θ A= 2 =loop area Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. B r I F B Interaction between electromagnet and a magnetic substance An electromagnet can be used to pick up a ferromagnetic material. The field of the electromagnet induces an alignment of the atomic scale dipoles resulting in a net force of attraction. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Does the compass needle rotate clockwise (cw), counterclockwise (ccw) or not at all? A. Clockwise B. Counterclockwise C. Not at all Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Does the compass needle rotate clockwise (cw), counterclockwise (ccw) or not at all? A. Clockwise B. Counterclockwise C. Not at all Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The magnetic field at the position P points A. Into the page. B. Up. C. Down. D. Out of the page. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The magnetic field at the position P points A. Into the page. B. Up. C. Down. D. Out of the page. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The positive charge is moving straight out of the page. What is the direction of the magnetic field at the position of the dot? A. Left B. Right C. Down D. Up Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The positive charge is moving straight out of the page. What is the direction of the magnetic field at the position of the dot? A. Left B. Right C. Down D. Up Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What is the current direction in this loop? And which side of the loop is the north pole? A. Current counterclockwise, north pole on bottom B. Current clockwise; north pole on bottom C. Current counterclockwise, north pole on top D. Current clockwise; north pole on top Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What is the current direction in this loop? And which side of the loop is the north pole? A. Current counterclockwise, north pole on bottom B. Current clockwise; north pole on bottom C. Current counterclockwise, north pole on top D. Current clockwise; north pole on top Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. An electron moves perpendicular to a magnetic field. What is the direction of ? A. Left B. Into the page C. Out of the page D. Up E. Down Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. An electron moves perpendicular to a magnetic field. What is the direction of ? A. Left B. Into the page C. Out of the page D. Up E. Down Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which magnet or magnets produced this induced magnetic dipole? A. a or d B. a or c C. b or d D. b or c E. any of a, b, c or d Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which magnet or magnets produced this induced magnetic dipole? A. a or d B. a or c C. b or d D. b or c E. any of a, b, c or d Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.