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Magnetism! Chapter 19

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Magnetic Poles and Magnetic Fields There are two magnetic poles, north and south. The north pole of a compass magnet is defined as the end that points towards the Earth’s north pole. Like poles repel, unlike poles attract. Magnetic poles come in pairs.

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Magnetic Poles and Fields Magnetic fields are drawn from north to south. Field lines that are closer together denote a stronger magnetic field. The direction of a magnetic field, B, at any location is given by the direction of the north pole of a compass needle. Magnetism is caused by moving electric charges!

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Magnetic Fields Magnetic field lines around a magnet – drawn from north to south. Magnetic field, B, is measured in N/Am or Tesla [T]

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Magnetic Field around Earth

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Magnetic Field Strength and Magnetic Force When a charged object moves in a magnetic field, B, a magnetic force acts on the charged object. When the velocity of the charge, v, is perpendicular to B, F = qvB and B = F/qv

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Magnetic Force F = qvB ; B = F/qv B is measured in N/(Cm/s) or N/Am [N/(Cm/s)] = [Tesla] = [T]

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Right Hand Rule For Direction of F m

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Magnetic Force F m When v and B are at right angles, F m = qvB When v and B are not at right angles, F m = qvBsinθ The magnetic force is perpendicular to both the velocity and to the magnetic field. Note: q is assumed positive

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Examples In a linear accelerator, a beam of protons travels horizontally northward. To deflect the protons eastward with a uniform magnetic field, the field should point in which direction? A particle with charge of –5.0 X 10 -4 C and mass of 2.0 X 10 -9 kg moves at a speed of 1.0 X 10 3 m/s in the + x direction. It enters a uniform magnetic field of 0.20 T that points in the +y direction. Which way will the particle deflect? What is the magnitude of the force on the particle? What is the radius of curvature?

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Homework Read Section 19.1 and 19.2 Do # 1 – 3, 6 – 8, 13, 15, 17, 18, 20. 21 on page 649

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Summary of Magnetic Force on Moving Charges When a charge moves at an angle with respect to a magnetic field, the charge feels a force of F = qvBsinθ The force is always perpendicular to both the velocity and the magnetic field. Magnetic force does not change speed, only direction When θ = 0, the charge feels no force.

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Summary of Magnetic Force on Moving Charges Charged particles traveling in a uniform magnetic field always have circular arcs as their trajectories.

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Applications An electron beam can be deflected by magnetic fields and can cause a fluorescent material to glow… Cathode-Ray Tubes are vacuum tubes that accelerate beams of electrons which are deflected by magnetic fields and cause a fluorescent screen to glow. Oscilloscopes, TV’s and computer monitors are made of cathode ray tubes.

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Applications A mass spectrometer uses magnetic fields to measure the mass of an ion (charged particle) It selects charged particles with a particular (known) velocity, then sends them into a uniform magnetic field where the radius of curvature can be measured. This allows for a calculation of the ion’s mass.

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Mass Spectrometer Parallel plates are set up perpendicular to magnetic fields. The only charges to go straight through without curving will be those for which F e = F m qE = qvB v = E/B

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Mass Spectrometer Text page 630

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Example One electron is removed from a methane molecule before it enters the mass spectrometer. After passing through the velocity selector, the ioni has a speed of 1.00 X 10 3 m/s. It then enters the main magnetic field region in which T = 6.70 X 10 -3 T. It follows a circular path in which it is detected 5.00 cm from the field entrance. Determine the mass of this molecule.

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Magnetic Force on Current Carrying Wire Since current is defined as moving charges, a wire carrying current in a magnetic field will feel a magnetic force. Consider a wire of length L F m = qvBsinθ and v = L/t F m =q(L/t)Bsinθ F m = (q/t)LBsinθ F m = ILBsinθ where θ give the angle between the current and the magnetic field

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Magnetic Force on Current Carrying Wire A wire of length L carrying a current, I, in a uniform magnetic field feels a total force F m = ILB sinθ The direction of the force can be found using the right hand rule

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Example Because a current carrying wire is acted on by a magnetic force, it would seem possible to suspend such a wire at rest above the ground using the Earth’s magnetic field. If a long straight wire is located at the equator, in what direction would the current have to be (up, down, east or west?) Calculate the current required to suspend the wire, assuming the Earth’s magnetic field is 0.40 G (gauss) at the equator and the wire is 1.0 meter long with mass of 30 grams. 1 G = 10 -4 T

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Homework Read 19.3, 19.4 Pay attention to Example 19.5 on page 635 Do # 22, 23, 30, 32, 36, 38, 42, 44, 45 – 48, 50 on page 651

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Magnetic Forces on Moving Charges Summary: F m = qvBsinθ F m = ILBsinθ

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Applications of Force on Current Carrying Wire Galvanometer! A loop of wire placed inside a magnetic field will feel a torque when a current passes through… Recall T = rFsinθ

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Galvanometers

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Galvanometer T = r Fsinθ Two forces create torque on a rectangular loop of length L and width w T net = 2r Fsinθ = 2(½w)(ILB)sinθ =wILBsinθ = AIBsinθ (A = area) For a coil of N turns, T net = NIABsinθ (m = NIA = magnetic moment)

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Galvanometer When a current is detected, the needle swings due the torque created by the magnetic force on the current carrying wire. A galvanometer with high resistance can be used as a voltmeter A galvanometer with low resistance can be used as an ammeter

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Other Applications of Current Carrying Wires in Magnetic Fields DC Motors - current passing through coil creates torque (spinning motion). The spinning is maintained by continually switching the direction of current. See page 636 diagram Electronic Balance – A downward force of gravity (the weight applied) is offset by an upward force created by coils in a magnetic field. The current needed to balance the weight is measured and converted into a ‘mass’ reading.

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Ampere’s Law Recall that magnetism is created by moving charges. Ampere’s Law – relates the current in a wire to the resulting magnetic field created by the moving charges in the wire Ampere’s Law can be used to find B near current carrying wires.

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Ampere’s Law Ampere’s Law allows us to find the magnetic field at some distance from a current carrying wire. Direction of B is found using right hand rule…

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Find Magnetic Field At a perpendicular distance, d, from a long straight wire, B(2πd) = µ 0 I where µ 0 is permeability of free space = 4π X 10 -7 Tm/A B = µ 0 I/2πd

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Find Magnetic Field At the center of a current carrying loop of radius r, B = µ 0 I/2r For a coil of N loops, B = µ 0 NI/2r

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Solenoid A solenoid is a coil of wire, length L, in which the interior magnetic field caused by current is constant and uniform. B = µ 0 NI/L

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Example The maximum household current in a wire is about 15 A. What are the magnitude and direction of the magnetic field the current produces 1.0 cm below the wire?

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Example A solenoid of 300 turns and length 0.30 m carries a current of 15.0 A. What is the magnitude and direction of the magnetic field at the center of the solenoid? Compare your result with the field near the single wire carrying the same current.

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Example: Two long parallel wires carry currents in the same direction. a) Is the magnetic force between the wires attractive or repulsive? Make a sketch to show your result. b) If both wires carry the same 5.0 A current, have length of 50 cm, and are separated by 30.0 mm, determine the force on each wire.

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Magnetic Materials Moving charges create magnetism One moving charge sets up a “magnetic domain” in the space around it. When a material has its magnetic domains aligned, the material acts like a magnet. Magnetic domains can be aligned using electric currents.

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Electromagnets Electromagnets are magnets which can be switched on or off. They set up a magnetic field inside a material using a current carrying coil.

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Electromagnets Recall B = µ 0 NI/L for solenoid where µ 0 = 4π X 10 -7 Now B = µNI/L for an electromagnet where μ = μ 0 κ m gives magnetic permeability and κ m gives the relative permeability of core

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Chapter 19 Summary Moving charges experience forces when placed in magnetic fields F m = qvBsinθ F m = ILBsinθ Moving charges set up magnetic fields! B = µ 0 I/2πd near long straight wire B = µ 0 NI/2r at center of circular loop B = µ 0 NI/L at center of a solenoid

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Homework Finish reading the chapter Page 654 # 83, 85, 92, 98, 104, 105, 106

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