a brief recap of the context…mcba11.phys.unsw.edu.au/~mcba/phys1231/firstlecture.pdflecture 7,...

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Today’s lecture:

PHYSICS 1B

Electricity & Magnetism

Magnetism

The Magnetic Field, B

Magnetic Forces

and

Motion in a Uniform Magnetic Field

Lecture 7, 04/12/2012

A Brief History of Magnetism…

PHYSICS 1B – Magnetism

Electricity & Magnetism – Magnetism

13th Century BC Records show that the Chinese used a compass with a magnetic needle, which is thought to have been an invention of either Arabic or Indian origin. 800 BC The Greeks discovered that the mineral magnetite (Fe3O4) attracts piece of iron.

Lecture 7, 04/12/2012




1269 Pierre de Maricourt found that the direction of a needle near a spherical natural magnet formed lines that encircled the sphere. Those lines also passed through two points diametrically opposed to each other. He called those points “poles” 1600 William Gilbert published the results of his experiments with magnetism, suggesting the Earth itself was a large, permanent magnet.

Lecture 7, 04/12/2012




1750 Experiments show that magnetic poles exert attractive or repulsive forces on each other. 1819 Hans Christian Oersted observed that an electric current deflected a compass needle during a physics demonstration. This revealed that there is a relationship between electricity and magnetism!

Every magnet, regardless of its shape, has two poles. We call these the north and south poles. Poles exert forces on each other, in much the same way that electric charges exert forces on each other. Like poles (and like charges) repel one another – i.e. N-N or S-S Unlike poles attract each other – i.e. N-S

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Magnetic Poles



The poles received their names due to the way a magnet behaves in the Earth’s magnetic field. If a bar magnet is suspended so that it can move freely, it will rotate. The magnetic north pole will point towards the Earth’s north geographic pole Which, a little perversely, means that the Earth’s north geographic pole is a magnetic south pole, and the Earth’s south geographic pole is a magnetic north pole!

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Magnetic Poles



The force between two poles varies as the inverse square of the distance between them. A single magnetic pole has never been isolated (i.e. magnetic poles are always found in pairs). All attempts to date to detect an isolated magnetic pole have been unsuccessful – although there is some theoretical basis for the existence of monopoles – single poles. No matter how often you cut a permanent magnet in two, each piece will always have a north and a south pole.

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Magnetic Poles, final



Remember – an electric field surrounds any electric charge. Similarly, a magnetic field surrounds any permanent magnet. In addition, the region of space surrounding any moving electric charge also contains a magnetic field.

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Magnetic Fields



The magnetic field is a vector quantity, and is symbolised by B The direction of B is given by that which the north pole of a compass needle points. Magnetic field lines trace this direction in space, and can be used to visualise the magnetic field. Just as electric field lines can be drawn to visualise the electric field!

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Magnetic Fields



If we were to take a compass and move it around a bar magnet, the compass arrow would turn in such a way that we could use it to trace out the magnetic field lines. Electric field lines ran from positive charges to negative charges. Magnetic field lines point from the magnet’s North pole to its South pole.

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Magnetic Fields around a Bar Magnet



Iron filings can be used to show the pattern of the magnetic field lines.

Remember – the direction of the field is the direction that a north pole would point.

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Magnetic Fields around a Bar Magnet



Again, iron filings can be used to show the pattern of the magnetic field lines.

Compare to the electric field produced by an electric dipole, as shown below:

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Magnetic Fields for Opposite Poles



Iron filings yet again…

Compare to the electric field produced by two like charges, as shown below:

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Magnetic Fields for Like Poles



More proper terminology would be that a magnet has “north-seeking” and “south-seeking” poles. The north-seeking pole points towards the north geographic pole (which corresponds to the Earth’s south magnetic pole). The south-seeking pole points towards the south geographic pole (which corresponds to the Earth’s north magnetic pole). The configuration of the Earth’s magnetic field is very much like that which would be achieved by burying a gigantic bar magnet deep in the Earth’s interior.

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Earth’s Magnetic Poles



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The source of the Earth’s magnetic field is thought to be convection currents in the Earth’s core. The magnetic field may well be the result of plate tectonics! Of the four terrestrial planets, Mercury, Venus, Earth and Mars, only the Earth has a strong magnetic field. The giant planets (Jupiter, Saturn, Uranus and Neptune) have much stronger fields than the Earth.

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It is well established that the direction of Earth’s magnetic field reverses periodically, on timescales of hundreds of thousands of years to a few million years (with the reversals typically thought to take between 1,000 and 10,000 years). Earth’s magnetic field protects Earth’s atmosphere and is the reason Aurorae are visible most frequently near the Earth’s magnetic poles.

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The Sun, on Sunday evening… (18th August, from http://spaceweather.com )

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Magnetic Field and Sunspots – a slight aside



http://spaceweather.com





The Sun, in 2001…

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Sunspots and the magnetic field of the Sun

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Coronal Loops in the Sun’s atmosphere – material follows the magnetic field lines.

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The magnetic field, B, at some point in space can be defined in terms of the magnetic force, FB. Note: B is sometimes known as the Magnetic Induction A magnetic force will be exerted on a charged particle moving in a magnetic field (with a velocity v). Assume, for now, that there are no gravitational or electric fields present…

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Magnetic Fields and Forces



The magnitude, FB , of the magnetic force exerted on the particle is proportional to both the charge, q, and the speed, v, of the particle. The direction of the force depends on the velocity of the particle and the direction of the magnetic field. The direction of the force is perpendicular to both the particle’s velocity, and the direction of the magnetic field. If the particles velocity vector makes any angle θ ≠ 0 with the field, the force therefore acts in a direction perpendicular to the plane formed by the velocity and the field.

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FB on a Charge Moving in a Magnetic Field



The magnetic force exerted on a positive charge is in the direction opposite the direction of the magnetic force exerted on a negative charge moving in the same direction. The magnitude of the magnetic force is proportional to the sine of the angle (θ) that the particle’s velocity makes with the direction of the magnetic field. i.e. 𝐹𝐵 ∝ sin 𝜃

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Mathematically, the magnetic force is expressed as: 𝑭𝑩 = 𝑞𝒗 × 𝑩 where: FB is the magnetic force q is the charge v is the velocity of the moving charge B is the magnetic field

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Direction



The rule is based on the right-hand rule for the cross product. Your thumb points in the direction of the force, if q is positive. The force is in the opposite direction to your thumb, if q is negative.

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Direction: The Right-Hand Rule



The magnitude of the magnetic force on a charged particle is:

𝐹𝐵 = 𝑞 𝑣 𝐵 sin 𝜃 Where θ is the angle between v and B FB is zero when v and B are parallel or antiparallel (i.e. if θ = 0⁰ or 180⁰). FB is a maximum when v and B are perpendicular (i.e. when θ = 90⁰)

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The Magnitude of FB.



A proton moves at a velocity v = 8 x 106 ms-1 in the x-direction. It enters a region with a magnetic field of B = 2.5 T directed at 60⁰ to the x-axis in the x-y-plane. What is the initial force on the proton? From the right hand rule, we know that the force acts in the z-direction.

𝐹 = 𝑞𝑣𝐵 sin 𝜃

∴ 𝐹 = 1.6 × 10−19 C . 8 × 106 ms−1 . 2.5 T . sin 60°

∴ 𝐹 = 2.77 × 10−12 N

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An Example.



1) Direction of force

The electric force acts along the direction of the electric field. The magnetic force acts perpendicular to the magnetic field.

2) Motion

The electric force acts on a charged particle regardless of whether it is moving. The magnetic force acts on a charged particle only when the particle is in motion.

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Differences Between Electric and Magnetic Fields



3) Work

The electric force does work in displacing a charged particle The magnetic force associated with a steady magnetic field does no work when a particle is displaced (since the force is perpendicular to the displacement at its points of application, and so F.ds = 0)

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Differences Between Electric and Magnetic Fields



The kinetic energy of a charged particle moving through a magnetic field cannot be altered by the magnetic field alone. When a charged particle moves with a given velocity through a magnetic field, the field can alter the direction of the velocity, but not the speed of the particle.

The kinetic energy of the particle is therefore not changed by the magnetic field.

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Work in Magnetic Fields



The SI unit of magnetic field is the tesla (T). Since we know that 𝐹𝐵 = 𝑞 𝑣 𝐵 sin 𝜃

1 T = 1 N

Cms

= 1 N

A m

Where A is the amp, which is the SI unit of electric current, which is Cs-1

You will sometimes here of magnetic fields measured in gauss (G) – this is the cgs unit of magnetic field, and 1 T = 104 G

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Units of Magnetic Field



When we want to represent magnetic field lines on a figure, there will be many occasions when those lines will either go into the page, or come out of it. The convention we use is that dots represent arrows that are coming out of the page, and crosses represent arrows going into the page. This is a standard notation, and can be used when plotting other vector quantities.

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A quick note on notation…



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Typical Magnetic Field Values



The north-pole end of a bar magnet is held near a positively charged piece of plastic. The plastic is: a) Attracted

b) Repelled

c) Unaffected by the magnet

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Quick Quiz



The north-pole end of a bar magnet is held near a positively charged piece of plastic. The plastic is: c) Unaffected by the magnet The magnetic force exerted by a magnetic field on a charge is proportional to the charge’s velocity relative to the field. If the charge is stationary, as in this situation, then there is no magnetic force.

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Quick Answer



A charged particle moves with velocity v in a magnetic field B. The magnetic force on the particle is a maximum when v is: a) Parallel to B

b) Perpendicular to B

c) Zero

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Quick Quiz



A charged particle moves with velocity v in a magnetic field B. The magnetic force on the particle is a maximum when v is:

b) Perpendicular to B

The maximum value of sin θ occurs when θ = 90⁰.

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Quick Answer



An electron moves in the plane of the screen towards the top of the screen. A magnetic field is also in the plane of the screen, directed to the right. The direction of the magnetic force on the electron is therefore: a) Toward the top of the screen

b) Toward the bottom of the screen

c) Toward the left edge of the screen

d) Toward the right edge of the screen

e) Out of the screen

f) Into the screen

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Quick Quiz



An electron moves in the plane of the screen towards the top of the screen. A magnetic field is also in the plane of the screen, directed to the right. The direction of the magnetic force on the electron is therefore: e) Out of the screen

The right hand rule gives the direction. Be sure to account for the negative charge on the electron!

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Quick Answer



a brief recap of the context…mcba11.phys.unsw.edu.au/~mcba/phys1231/firstlecture.pdflecture 7,...

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