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Physics Lecture Resources Prof. Mineesh Gulati Head-Physics Wing Happy Model Hr. Sec. School, Udhampur, J&K Website: happyphysics.com happyphysics.com Ch 27 Magnetic Field and Magnetic Forces © 2005 Pearson Education 27.1 Magnetism © 2005 © 2005 Pearson Pearson Education Education © 2005 © 2005 Pearson Pearson Education Education Earth’s magnetic field © 2005 © 2005 Pearson Pearson Education Education N S Break apart N S N S Break apart N S N S N S © 2005 © 2005 Pearson Pearson Education Education N S © 2005 © 2005 Pearson Pearson Education Education 27.2 Magnetic Field Magnetic interactions: 1. A moving charge or a current creates a magnetic field in the surrounding space 2. The magnitude field exerts a force on any other moving charge or current that is present in the field © 2005 © 2005 Pearson Pearson Education Education © 2005 © 2005 Pearson Pearson Education Education F qv B © 2005 © 2005 Pearson Pearson Education Education © 2005 © 2005 Pearson Pearson Education Education Units of B-field Unit of B-field is tesla 1 tesla = 1 T =1 N/Am Another unit is gauss (G) © 2005 © 2005 Pearson Pearson Education Education 27.3 Magnetic Field Lines and Magnetic Flux F qv B © 2005 © 2005 Pearson Pearson Education Education © 2005 © 2005 Pearson Pearson Education Education Magnetic Flux and Gauss’s Law for Magnetism magnetic flux through any closed surface B dA 0 magnetic flux through a surface B B dA B cos dA B dA © 2005 © 2005 Pearson Pearson Education Education Example 27.2 The figure shows a flat surface with area 3cm2 in a uniform B-field. If the magnetic flux through this area is 0.9mWb, Find the magnitude of B-field. ANS: B B A cos 0.9 103Wb (3.0 104 m 2 )(cos 60) 6T © 2005 Pearson Education 27.4 Motion of Charged Particles in a Magnetic Field Motion of a charged particle under the action of a magnetic field alone is always motion with constant speed v2 F m R mv R qB © 2005 © 2005 Pearson Pearson Education Education Magnetic bottle © 2005 © 2005 Pearson Pearson Education Education Example 27.3 A magnetron in a microwave oven emits electromagnetic waves with frequency f=2450MHz. What magnetic field strength is required for electrons to move in circular paths with this frequency? ANS: m B q 31 1 (9.1110 kg )(1.54 10 s ) 1.60 1019 C 0.0877T © 2005 Pearson Education 10 27.5 Applications of Motion of Charged Particles Velocity Selector Thomson’s e/m Experiment Mass Spectrometers © 2005 © 2005 Pearson Pearson Education Education 27.6 Magnetic Force on a Current-Carrying Conductor J nqvd JA I F IlB © 2005 © 2005 Pearson Pearson Education Education magnetic force on a straight wire segment F Il B magnetic force on an infinitesimal wire section dF I dl B © 2005 © 2005 Pearson Pearson Education Education 27.7 Force and Torque on a Current Loop magnitude of torque on a current loop τ IBA sin vector torque on a current loop τ μ B potential energy for a magnetic dipole U μ B B cos © 2005 © 2005 Pearson Pearson Education Education © 2005 © 2005 Pearson Pearson Education Education 27.8 The Direct-Current Motor © 2005 © 2005 Pearson Pearson Education Education © 2005 © 2005 Pearson Pearson Education Education 27.9 The hall Effect nq J x By Ez © 2005 © 2005 Pearson Pearson Education Education Magnetic interactions are fundamentally interactions between moving charged particles. These interactions are described by the vector magnetic field, denoted by B .A particle with charge q moving with velocity v in a magnetic field B experiences a force F that is perpendicular to both v and B . The SI unit of magnetic field is the tesla (1 T = 1 N/A.m). (See Example 28.1) © 2005 © 2005 Pearson Pearson Education Education A magnetic field can be represented graphically by magnetic field lines. At each point a magnetic field line is tangent to the direction of B at that point. Where field lines are close together the field magnitude is large, and vice versa. © 2005 © 2005 Pearson Pearson Education Education Magnetic fluxΦB through an area is defined in an analogous way to electric flux. The SI unit of magnetic flux is the weber (1 Wb = 1Tm2). The net magnetic flux through any closed surface is zero (Gauss’s law for magnetism). As a result, magnetic field lines always close on themselves. (See Example 27.2) © 2005 © 2005 Pearson Pearson Education Education The magnetic force is always perpendicular to v ; a particle moving under the action of a magnetic field alone moves with constant speed. In a uniform field, a particle with initial velocity perpendicular to the field moves in a circle with radius R that depends on the magnetic field moves in a circle with radius R that depends on the magnetic field strength B and the particle mass m, speed v, and charge q. (See Examples 27.3 and 27.4) © 2005 © 2005 Pearson Pearson Education Education Crossed electric and magnetic fields can be used as a velocity selector. The electric and magnetic forces exactly cancel when v = E/B. (See Examples 27.5 and 27.6) © 2005 © 2005 Pearson Pearson Education Education A straight segment of a conductor carrying current I in a magnetic field B experiences a forceF that is perpendicular to both B and the vector l, which points in the direction of the current and has magnitude equal to the length of the segment. A similar relationship gives the force d F on an infinitesimal current-carrying segment d l . © 2005 © 2005 Pearson Pearson Education Education A current loop with area A and current I in a uniform magnetic fieldB experiences no net magnetic force, but does experience a magnetic torque of magnitude τ . The vector torque can be expressed in terms of the magnetic moment IA of the loop, as can the potential energy U of a magnetic moment in a magnetic field B . The magnetic moment of a loop depends only on the current and the area; it is independent of the shape of the loop. © 2005 © 2005 Pearson Pearson Education Education In a dc motor a magnetic field exerts a torque on a current in the rotor. Motion of the rotor through the magnetic field causes and induced emf called a back emf. For a series motor, in which the rotor coil is in parallel with coils that produce the magnetic field, the terminal voltage is the sum of the back emf and the drop Ir across the internal resistance. © 2005 © 2005 Pearson Pearson Education Education The Hall effect is a potential difference perpendicular to the direction of current in a conductor, when the conductor is placed in a magnetic field. The Hall potential is determined by the requirement that the associated electric field must just balance the magnetic force on a moving charge. Hall-effect measurements can be used to determine the sigh of charge carriers and their concentration n. © 2005 © 2005 Pearson Pearson Education Education END Visit: happyphysics.com For Physics Resources