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MAGNETISM History of Magnetism Bar Magnets Magnetic Dipoles Magnetic Fields Magnetic Forces on Moving Charges and Wires Electric Motors Current Loops and

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MAGNETISM History of Magnetism Bar Magnets Magnetic Dipoles Magnetic Fields Magnetic Forces on Moving Charges and Wires Electric Motors Current Loops and Electromagnets Solenoids Sources of Magnetism Spin & Orbital Dipole Moments Permanent Magnets Earths Magnetic Field Magnetic Flux Induced Emf and Current Generators Crossed Fields Slide 2 History of Magnetism The first known magnets were naturally occurring lodestones, a type of iron ore called magnetite (Fe 3 O 4 ). People of ancient Greece and China discovered that a lodestone would always align itself in a longitudinal direction if it was allowed to rotate freely. This property of lodestones allowed for the creation of compasses two thousand years ago, which was the first known use of the magnet. In 1263 Pierre de Maricourt mapped the magnetic field of a lodestone with a compass. He discovered that a magnet had two magnetic poles North and South poles. In the 1600's William Gilbert, physician of Queen Elizabeth I, concluded that Earth itself is a giant magnet. In 1820 the Danish physicist Hans Christian rsted discovered an electric current flowing through a wire can cause a compass needle to deflect, showing that magnetism and electricity were related. Slide 3 History (cont.) In 1830 Michael Faraday (British) and Joseph Henry (American) independently discovered that a changing magnetic field produced a current in a coil of wire. Faraday, who was perhaps the greatest experimentalist of all time, came up with the idea of electric and magnetic fields. He also invented the dynamo (a generator), made major contributions to chemistry, and invented one of the first electric motors In the 19th century James Clerk Maxwell, a Scottish physicist and one of the great theoreticians of all times, mathematically unified the electric and magnetic forces. He also proposed that light was electromagnetic radiation. In the late 19 th century Pierre Curie discovered that magnets loose their magnetism above a certain temperature that later became known as the Curie point. In the 1900's scientists discover superconductivity. Superconductors are materials that have a zero resistance to a current flowing through them when they are a very low temperature. They also exclude magnetic field lines (the Meissner effect) which makes magnetic levitation possible. Slide 4 Magnetic Dipoles Recall that an electric dipole consists of two equal but opposite charges separated by some distance, such as in a polar molecule. Every magnet is a magnetic dipole. A bar magnet is a simple example. Note how the E field due an electric dipole is just like the magnetic field ( B field) of a bar magnet. Field lines emanate from the + or N pole and reenter the - or S pole. Although they look the same, they are different kinds of fields. E fields affect any charge in the vicinity, but a B field only affects moving charges. As with charges, opposite poles attract and like poles repel. + _ - N S Electric dipole and E field Magnetic dipole and B field Slide 5 Magnetic Monopole Dont Exist We have studied electric fields to due isolated + or - charges, but as far as we know, magnetic monopole do not exist, meaning it is impossible to isolate a N or S pole. The bar magnet on the left is surrounded by iron filings, which orient themselves according to the magnetic field they are in. When we try to separate the two poles by breaking the magnet, we only succeed in producing two distinct dipoles (pic on right). Bar magnet demo Slide 6 Magnetic Fields You have seen that electric fields and be uniform, nonuniform and symmetric, or nonuniform and asymmetric. The same is true for magnetic fields. (Later well see how to produce uniform magnetic fields with a current flowing through a coil called a solenoid.) Regardless of symmetry or complexity, the SI unit for any E field is the N/C, since by definition an electric field is force per unit charge. Because there are no magnetic monopoles, there is no analogous definition for B. However, regardless of symmetry or complexity, there is only one SI unit for a B field. It is called a tesla and its symbol is T. The coming slides will show how to write a tesla in terms of other SI units. The magnetic field vector is always tangent to the magnetic field. Unlike E fields, all magnetic field lines that come from the N pole must land on the S pole--no field lines go to or come from infinity. Slide 7 Force Due to Magnetic Field The force exerted on a charged particle by a magnetic field is given by the vector cross product: F = q v B sin F = force (vector) q = charge on the particle (scalar) v = velocity of the particle relative to field (vector) B = magnetic field (vector) F = q v B Recall that the magnitude of a cross is the product of the magnitudes of the vectors times the sine of the angle between them. So, the magnitude of the magnetic force is given by where is angle between q v and B vectors. Slide 8 Cross Product Review Let v 1 = x 1, y 1, z 1 and v 2 = x 2, y 2, z 2 . By definition, the cross product of these vectors (pronounced v 1 cross v 2 ) is given by the following determinant. v1 v2 =v1 v2 = x 1 y 1 z 1 x 2 y 2 z 2 i j k = (y 1 z 2 - y 2 z 1 ) i - (x 1 z 2 - x 2 z 1 ) j + (x 1 y 2 - x 2 y 1 ) k Note that the cross product of two vectors is a vector itself that is to each of the original vectors. i, j, and k are the unit vectors pointing, along the positive x, y, and z axes, respectively. (See the vector presentation for a review of determinants.) Slide 9 a b a b. Right Hand Rule Review b a a b A quick way to determine the direction of a cross product is to use the right hand rule. To find a b, place the knife edge of your right hand (pinky side) along a and curl your hand toward b, making a fist. Your thumb then points in the direction of It can be proven that the magnitude of is given by: a b sin | a b | = where is the angle between a and b. Slide 10 Magnetic Field Units A magnetic field of one tesla is very powerful magnetic field. Sometimes it may be convenient to use the gauss, which is equal to 1/10,000 of a tesla. Earths magnetic field, at the surface, varies but has the strength of about one gauss. 1 N = 1 C (m / s) (T) F = q v B sin From the formula for magnetic force we can find a relationship between the tesla and other SI units. The sine of an angle has no units, so 1 T = 1 N1 N C (m / s) 1 N1 N A mA m = Slide 11 Direction of Magnetic Field & Force B + Near the poles, where the field lines are close together, the field is very strong (so the field vector are drawn longer). Anywhere in the field the mag. field vector is always tangent to the mag. field line there. The + charge in the pic in moving into the page. Since q is +, the q v vector is also into the page. The - charge is moving to the right, so the q v vector is to the left. The mag. force vector is always to plane formed by the q v vector and the B vector. B - v F The force on the - charge is into the page. If a charge is motionless relative to the field, there is no magnetic force on it, but if either a magnet is moving or a charge is moving, there could a force on the charge. If a charge moves parallel to a magnetic field, there is no magnetic force on it, since sin 0 = 0. Slide 12 Magnetic Field & Force Practice Find the direction of the magnetic force or velocity: 1.A + charge at P is moving out of the page. 2.A - charge at Q is moving out of the page. 3.A - charge at Q is moving to the right. 4.A + charge at Q is moving up. 5.A - charge at R is moving up and to the left. 6.A + charge at R is moving down and to the right. 7.A - charge at R feels a force into the page. 8.A + charge at P feels a force out of the page. 9.A - charge at Q feels an upward force. P Q R Slide 13 Magnetic Force Sample Problem N S N + 5 m/s This magnet is similar to a parallel plate capacitor in that there is a strong uniform field between its poles with some fringing on the sides. Suppose the magnetic field strength inside is 0.07 T and a 4.3 mC charge is moving through the field at right angle to the field lines. How strong and which way is the magnetic force on the charge? Answer: F = q v B F = q v B since sin 90 = 1. So, F = 0.0015 N directed out of the page. Slide 14 Motion of a Charge in a Magnetic Field The s represent field lines pointing into the page. A positively charged particle of mass m and charge q is shot to the right with speed v. By the right hand rule the magnetic force on it is up. Since v is to B, F = F B = q v B. Because F is to v, it has no tangential component; it is entirely centripetal. Thus F causes a centripetal acceleration. As the particle turns so do v and F, and if B is uniform the particle moves in a circle. This is the basic idea behind a particle accelerator like Fermilab. Since F is a centripetal force, F = F C = m v 2 / R. Lets see how speed, mass, charge, v + q, m F B R field strength, and radius of curvature are related: F B = F C q v B = m v 2 / R m vm v R = q Bq B Slide 15 Magnetic Force on a Current Carrying Wire S N I A section of wire carrying current to the right is shown in a uniform magnetic field. We can imagine positive charges moving to right, each feeling a magnetic force out of the page. This will cause the wire to bow outwards. Shown on the right is the view as seen when looking at the N pole from above. The dots represent a uniform I...... B mag. field coming out of the page. The mag. force on the wire is proportional to the field strength, the current, and the length of the wire. Continued Slide 16 Magnetic Force on a Wire (cont.) F = q v B F = (q / t ) v t B F = I L B I...... B Current is the flow of positive charge. As a certain amount of charge, q, moves with speed v through a wire of length L, the force of this quantity of charge is: Over the time period t required for the charge to traverse the length of the wire, we have: Since q / t = I and v t = L, we can write:

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