1 Chapter 22 Magnetism2 Overview of Chapter 22 • The Magnetic Field • The Magnetic Force on Moving Charges • The Motion of Charged Particles in a Magnetic Field • The Magnetic Force Exerted on a Current-Carrying Wire • Loops of Current and Magnetic Torque3 Overview of Chapter 22 • Electric Currents, Magnetic Fields • Current Loops and Solenoids • Magnetism in Matter4 22-1 The Magnetic Field Permanent bar magnets have opposite poles on each end, called north and south. Like charges repel; opposites attract. If a magnet is broken in half, each half has two poles:5 22-1 The Magnetic Field The magnetic field can be visualized using magnetic field lines, similar to the electric field. If iron filings are allowed to orient themselves around a magnet, they follow the field lines.6 22-1 The Magnetic Field • Magnetic field lines exit from the north pole of a magnet and enter at the south pole… • Like electric fields, denser lines mean stronger field..7 22-1 The Magnetic Field • The Earths magnetic field resembles that of a bar magnet. • Since the north poles of compass needles point towards the north… - Magnetic pole there actually is a south pole…8 22-2 The Magnetic Force on Moving Charges • The Force is perpendicular to both velocity and magnetic field direction.. • θ is angle between velocity and magnetic field directions…9 22-2 The Magnetic Force on Moving Charges The magnetic force on a moving charge is actually used to define the magnetic field:10 22-2 The Magnetic Force on Moving Charges • Right-hand rule helps us determine direction of the force… • Applies to positive charge, forces in other direction for negative charge… - Thumb=Force - Forefinger=velocity - Index finger=Magnetic field11 22-2 The Magnetic Force on Moving Charges This relationship between the three vectors – magnetic field, velocity, and force – can also be written as a vector cross product:12 22-3 The Motion of Charged Particles in a Magnetic Field • Positively charged particle in an electric field experiences a force in the direction of the field • In a magnetic field the force is perpendicular to the field…13 22-3 The Motion of Charged Particles in a Magnetic Field • Because the magnetic force is always perpendicular to the direction of motion, the path of a particle is circular. • An electric field can do work on a particle, a magnetic field cannot… • Particles speed remains constant • Therefore kinetic energy remains constant.14 22-3 The Motion of Charged Particles in a Magnetic Field For a particle of mass m and charge q, moving at a speed v in a magnetic field B, the radius of the circle it travels is:15 22-3 The Motion of Charged Particles in a Magnetic Field In a mass spectrometer, ions of different mass and charge move in circles of different radii, allowing separation of different isotopes of the same element.16 22-3 The Motion of Charged Particles in a Magnetic Field At the STAR experiment, we also use this to measure momentum of particles… momentum r1 r217 22-3 The Motion of Charged Particles in a Magnetic Field • If a particles velocity makes an angle with the magnetic field… • Component of the velocity along the magnetic field will not change… • Particle with an initial velocity at an angle to the field will move in a helical path….18 22-4 The Magnetic Force Exerted on a Current-Carrying Wire The force on a segment of a current-carrying wire in a magnetic field is given by: L=length of wire Use right hand rule again to figure out direction of force19 22-5 Loops of Current and Magnetic Torque In the current loop shown, the vertical sides experience forces that are equal in magnitude and opposite in direction. They create a torque around the vertical axis of the loop. Recap: Torque is a rotational force.. r F20 22-5 Loops of Current and Magnetic Torque The total torque is the sum of the torques from each force: Or, since A = hw, A is area of loop21 22-5 Loops of Current and Magnetic Torque If the plane of the loop is at an angle to the magnetic field,22 22-5 Loops of Current and Magnetic Torque To increase the torque, a long wire may be wrapped in a loop many times, or turns. If the number of turns is N, we have23 22-5 Loops of Current and Magnetic Torque The torque on a current loop is proportional to the current in it, which forms the basis of a variety of useful electrical instruments. Here is a galvanometer:24 22-6 Electric Currents, Magnetic Fields Experimental observation: • Electric currents can create magnetic fields. • These fields form circles around the current…..25 22-6 Electric Currents, Magnetic Fields To find the direction of the magnetic field due to a current-carrying wire… • Point the thumb of your right hand along the wire in the direction of the current I…. • Fingers are now curling around the wire in the direction of the magnetic field….26 22-6 Electric Currents, Magnetic Fields The magnetic field is inversely proportional to the distance from the wire:27 22-6 Electric Currents, Magnetic Fields We can use Ampères Law to find the magnetic field around a long, straight wire:28 22-6 Electric Currents, Magnetic Fields Since a current-carrying wire experiences a force in a magnetic field, and a magnetic field is created by a current-carrying wire, there is a force between current-carrying wires:29 22-7 Current Loops and Solenoids The magnetic field of a current loop is similar to the magnetic field of a bar magnet. In the center of the loop,30 22-7 Current Loops and Solenoids A solenoid is a series of current loops formed into the shape of a cylinder:31 22-8 Magnetism in Matter • Electrons surrounding an atom create magnetic fields through their motion. • Fields usually are in random directions and have no net effect… - But in some atoms there is a net magnetic field. • If the atoms have a strong tendency to align with each other, creating a net magnetic field… - Material is called ferromagnetic.32 22-8 Magnetism in Matter • Ferromagnets are characterized by domains, which each have a strong magnetic field - Randomly oriented... • In the presence of an external magnetic field, the domains align… - Creates magnetic field within the material…33 22-8 Magnetism in Matter • Permanent magnets are ferromagnetic… • Such materials can preserve a
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