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Magnetic Force Physics 102 Professor Lee Carkner Lecture 17

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PAL #17 Magnetic Field Direction electron is fired into magnetic field that points north if it is deflected up Force equation: F = qvB sin = sin -1 (F/qvB) = sin -1 [(1.7X10 -14 )/((1.6X10 -19 )(3X10 5 )(0.5))] = sin -1 (0.708) = 45 degrees v vector points 45 west of north, which is pointed northwest, so electron was fired from southeast

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Electron in B Field v B North West South East From right hand rule: B is north and force is up so v is from west (reversed to east for electron)

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Electric and Magnetic Force How do the electric and magnetic forces differ? Dependences Magnetic force depends on v and , as well as B and q Vector Force vector does change for a magnetic field, since as the particle is deflected, the v vector changes Electric fields accelerate particles, magnetic fields deflect particles

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Particle Motion A particle moving freely in a magnetic field will have one of three paths, depending on Straight line Circle Helix This assumes a uniform field that the particle does not escape from

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Circular Motion How big is the circle? Magnetic force is F = Centripetal force is F = We can combine to get r = mv/qB Since the path is a circle, the total path length for one orbit is the circumference (=2 p r)

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Circle Properties Circle radius is inversely proportional to q and B r is directly proportional to v and m Can use this idea to make mass spectrometer Send mixed atoms through the B field they will come out separated by mass

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Helical Motion Charged particles will spiral around magnetic field lines If the field has the right geometry, the particles can become trapped Since particles rarely encounter a field at exactly 0 or 90 degrees, such motion is very common Examples: Gyrosynchrotron radio emission from planets and stars

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Helical Motion

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Solar Wind Particles in Earth’s Magnetic Field

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Magnetic Field and Current Since a current is moving charge, a magnet will produce a force on a wire with a current flowing through it So qv = IL, thus: F = BIL sin We can use the right hand rule to get the direction of the force Use the direction of the current instead of v

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Force on a Wire

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Force on a Loop of Wire Consider a loop of wire placed so that it is lined up with a magnetic field Two sides will have forces at right angles to the loop, but in opposite directions The loop will experience a torque

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Torque on Loop For a loop of width w and height h, force is F = BIL sin for each long side F = BIh The torque is the force times the moment arm (distance to the center), which is w/2 but hw is the area of the loop, A = IBA = IBA sin Note that is the angle between the B field and a vector normal to the face of the loop

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Torque on Loop

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General Loops If there are multiple loops (N), the torque is the sum of each = IBAN sin A loop placed along a magnetic field will try to align such that the field goes straight through it If you reverse the direction of the current at just the right time you can get the coil to spin Can harness the spin to do work

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Next Time Exam #3 Monday For next Wednesday Read 20.7-20.8 Homework: Ch 20, P 4, 17, 48, 49

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A beam of electrons is pointing right at you. What direction would a magnetic field have to have to produce the maximum deflection in the right direction? A)Right B)Left C)Up D)Down E)Right at you

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A beam of electrons is pointing right at you. What direction would a magnetic field have to have to produce the maximum deflection in the up direction? A)Right B)Left C)Up D)Down E)Right at you

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A beam of electrons is pointing right at you. What direction would a magnetic field have to have to produce no deflection? A)Right B)Left C)Up D)Down E)Right at you

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