Chapter 22: Magnetism

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Chapter 22: Magnetism Magnets Magnets are caused by moving charges. Permanent Magnets vs.

north pole is what kind of pole? But any pole attracts metal: Why? Bar magnets are dipoles.

analogously to the electric field Is there an analog to Coulomb s Law?

1 Chapter 22: Magnetism Magnets Magnets are caused by moving charges. Permanent Magnets vs. Electromagnets Magnets always have two poles, north and south. Like poles repel, opposites attract. Brent Royuk Phys-112 Concordia University 2 Magnets North means north-seeking, so Earth s north pole is what kind of pole? But any pole attracts metal: Why? Bar magnets are dipoles. Can there be a monopole? History: lodestones and magnetic compasses. Remember Magnesia? Permanent magnets vs. electromagnets: More later Magnetic Fields The magnetic field B surrounds magnets analogously to the electric field Is there an analog to Coulomb s Law? No, the B- field is more complicated. 3 4 B-Field Lines Field line mapping: What defines a field line? The direction of the line is always from N to S. Earth s Magnetic Field Probably caused by currents in Earth s molten core Drift and reversals Last reversal: 780,000 years ago N S 5 6 1

Units [B] = [F/qv] 1 N/Am 1 tesla (T) Neutron star: 10 8 Big magnet: 1.5 Small bar magnet:.

2 What s Wrong With This Picture? Magnetic Force on a Moving Charge A moving charge moving in a perpendicular direction through a B-field experiences a force perpendicular to its motion Qualitative: F qvb sin θ 7 8 Electric Field Units [B] = [F/qv] 1 N/Am 1 tesla (T) Neutron star: 10 8 Big magnet: 1.5 Small bar magnet:.01 T Interstellar space: Magnetically shielded laboratory: Another unit: 1 T = 10 4 gauss (G) Earth s magnetic field: 0.5 G Magnetic Force on a Moving Charge F = qvb sin θ Note that the force is maximum when perpendicular, minimum at parallel. Weird. What is the significance of a field line for a moving charge? Example: An electron moves at right angles to a magnetic field of 0.12 T. What is its speed if the force exerted on it is 8.9 x N? 9 10 Direction of the Magnetic Force F = q(v x B) Math note: The parentheses are unnecessary The Right Hand Rule Wrap or Point methods In/Out conventions Positive vs. Negative particles What s Wrong With This Picture?

Examples What direction is the force acting on a charged particle traveling west through Earth s magnetic field? Down? South? A charge of +2.

An electron moving with a speed of 9.1 x 10 5 m/s in the positive x direction experiences zero magnetic force. When it moves in the positive y direction, it experiences a force of 2.

Motion of Charged Particles in B-Fields How will a charged particle move through a B-field? Find the radius.

3 Examples What direction is the force acting on a charged particle traveling west through Earth s magnetic field? Down? South? A charge of +2.5 µc moves at 55 m/s left-to-right across the blackboard through a region with a field of T that is out of the board. What force acts on it? What if the particle is charged negatively? An electron moving with a speed of 9.1 x 10 5 m/s in the positive x direction experiences zero magnetic force. When it moves in the positive y direction, it experiences a force of 2.0 x N that points in the negative z direction. What is the direction and magnitude of the magnetic field? Magnets and big old CRT screens. Motion of Charged Particles in B-Fields How will a charged particle move through a B-field? Find the radius Motion of Charged Particles in B-Fields Helical motion of charged particles from the sun (the solar wind). Velocity Selector Traveling through crossed electric and magnetic field, a charged particle feels two forces: qvb and qe. If the forces are equal, E = vb and there s no net force. v = E/B Mass Spectrometer The radius of the trajectory measures the mass. But you must also know the charge. Singly, doubly ionized? Start with: F = qvb sin θ Force on a Wire q = It = IL/v, so F = ILB sin θ Vector equivalent: F = I(L x B)

Force on a Wire A Linear Motor Which way would the bar move? Force on a Wire In the picture below, the wire is deflected downward.

0500 kg is suspended from two thin flexible wires as shown below. At right angles to the rod is a uniform magnetic field of 0.

Application: Loudspeakers A modulated current is sent to a voice coil, which experiences a force from a magnet that is transmitted onto a speaker

4 Force on a Wire A Linear Motor Which way would the bar move? Force on a Wire In the picture below, the wire is deflected downward. Which side of the magnet is a north pole? The monstrosity The Levitating Wire A copper rod m long and with a mass of kg is suspended from two thin flexible wires as shown below. At right angles to the rod is a uniform magnetic field of T pointing into the picture. Find a) the direction and b) the magnitude of the electric current needed to levitate the copper rod. Application: Loudspeakers A modulated current is sent to a voice coil, which experiences a force from a magnet that is transmitted onto a speaker cone Current Loops A Rectangular Loop Current Loops Generally, any current-carrying loop in a magnetic field experiences a torque equal to: τ = NIAB sin θ This law also follows a righthand rule

Current Loop Example Use τ = NIAB sin θ to find the torque on the loop below if I = 0.22 A and B = 0.050 T.

25 26 Electromagnets The Long, Straight Wire How long is it?

both wires, b) below both wires, and c) between the wires? 27 28 Solenoids What is the direction of the B-field in the vicinity of a current-carrying loop?

29 Magnetic Materials Permanent magnets can create magnet fields with spinning electrons. In ferromagnetic materials like Fe and Ni this tendency is strong.

5 Current Loop Example Use τ = NIAB sin θ to find the torque on the loop below if I = 0.22 A and B = T. Application: The Galvanometer Torque on a coil of current loops is balanced by a spring. Galvanometers can be configured as voltmeters or ammeters Electromagnets The Long, Straight Wire How long is it? B = µ o I 2πr The Permeability of Free Space: µ o = 4π x 10-7 Tm/A Demo Another Right- Hand Rule: Long Straight Wire What direction is the B-field a) above both wires, b) below both wires, and c) between the wires? Solenoids What is the direction of the B-field in the vicinity of a current-carrying loop? The field at the center of a solenoid: B = µ IN o = µ o ni; n N L L Demo Do two parallel currentcarrying wires attract or repel each other? 29 Magnetic Materials Permanent magnets can create magnet fields with spinning electrons. In ferromagnetic materials like Fe and Ni this tendency is strong. Materials lose their magnetism above the Curie Temperature (770 o C for Fe). Ferromagnetic cores magnify the field in a solenoid. Diamagnetic materials become magnetic in response to B-fields. Paramagnetic materials do as well, but their B-field opposes the applied field. All materials display some paramagnetism. 30 5

6 Ferromagnetic Materials Domain Formation Creating and destroying temporary ferromagnets Electromagnet Summary

Chapter 22: Magnetism. Brent Royuk Phys-112 Concordia University

Chapter 22: Magnetism. Brent Royuk Phys-112 Concordia University Chapter 22: Magnetism Brent Royuk Phys-112 Concordia University Magnets Magnets are caused by moving charges. Permanent Magnets vs. Electromagnets Magnets always have two poles, north and south. Like poles