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Magnets PH 203 Professor Lee Carkner Lecture 26 Magnetic Materials The moving charges in a magnet are spinning or orbiting electrons Problem: The most common and well-known examples of magnetism result from extremely complex physics Dipolar Field No Magnetic Monopoles Like Repel, Opposites Attract Dipoles = mB sin q U = -mB cos q When aligned with the field the energy is –mB, at right angles to the field the energy is 0, when opposite the field the energy is +mB Dipoles that are not aligned with the field will turn until they are Spin Magnetic Dipole We can write this as ms = mB = (eh/4pm) = 9.27X10-24 J/T The electron can feel a torque and has magnetic potential energy just like a normal magnetic dipole Orbital Magnetic Dipole The orbital angular momentum is quantized We can write the orbital magnetic dipole moment as morb = -mlmB where mB is again the Bohr magneton and ml is the orbital magnetic quantum number (0, 1, 2, 3 …) Magnetic Energy Like any magnetic dipole (e.g., a loop of current) U = -mBext where potential energy is minimum Note that the total energy between parallel and anti-parallel spins is 2 mBext Diamagnetism Net orbital magnetic dipole moment is zero Like a bunch of loops with half with clockwise and half with counterclockwise currents Speeds up electrons one way, slows down electrons other way Almost all materials are diamagnetic, but the net effect is usually very weak Paramagnetism But they are usually randomly aligned and so there is no net magnetic field An external magnetic field will cause the atomic dipole moments to try to align Thermal motions of the material try to randomize the atoms Curie’s Law For low temperatures M can be found from Curie’s Law M = C(Bext/T) Where C is the Curie constant Strong magnetic fields and low temperatures produce more paramagnetism Ferromagnetism Due to an effect called exchange coupling, the electron spins of nearby atoms align with each other Appling an external magnetic field can cause these domains to permanently align The Earth’s Magnetic Field The Earth has a magnetic field produced by the dynamo effect We can find the direction of the Earth’s magnetic field with a small bar magnet called a compass The Earth’s “north magnetic pole” is really a the south pole of a magnet! Earth as a Magnet Jupiter’s Magnetosphere Planets and Magnetism A planet will have a magnetic field if: It has a conducting liquid interior It has a fast enough rotation This interaction region is known as the magnetosphere Next Time Final exam, Thursday, 9am To step down 120 household current to 12 volts, we would need a transformer with a ratio of turns between the primary and secondary transformer of, A) B) C) D) E) 1 to 1 10 to 1 12 to 1 100 to 1 120 to 1 What is the direction of the magnetic field in the PAL at a point due east of the center of the region? A) B) C) D) E) North South East West Up Consider a standard 6-sided die. Suppose the magnetic flux through each side 1-5 is equal to the number of spots on the side (in Wb) and points outward for even sides and inward for odd. What is the flux magnitude through the side with 6 spots? A) B) C) D) E) 1 Wb 2 Wb 3 Wb 6 Wb 9 Wb Consider 3 Gaussian surfaces. (1) encloses the north pole of a bar magnet, (2) encloses the south pole of a bar magnet, and (3) encloses the entire bar magnet. Rank the surfaces according to the total magnetic flux through them, greatest first. A) B) C) D) E) 1, 2, 3 3, 2, 1 2, 1, 3 1, 3, 2 All tie