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## Magnetic Force

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**Magnetic Force**PH 203 Professor Lee Carkner Lecture 16**Charge Carriers**Imaging a current flowing from top to bottom in a wire, with a magnetic field pointing “in” If the charge carriers are negative (moving to the top), the magnetic field will also deflect them to the right**The Hall Effect**If it is high the carriers are positive Since a voltmeter shows the low potential is on the right, the electron is negative**Hall Quantified**Electrons are now longer deflected and the potential across the strip is constant but the velocity is the drift speed of the electrons v = i/neA n = Bi/eAE Since the potential V = Ed and the thickness of the strip (lower case “ell”), l = A/d n = Bi/Vle**Electric and Magnetic Force**• For a uniform field, electric force vector does not change • Electric fields accelerate particles, magnetic fields deflect particles**Particle Motion**• A particle moving freely in a magnetic field will have one of three paths, depending on q • Straight line • When q = • Circle • When q = • Helix • When • This assumes a uniform field that the particle does not escape from**Circular Motion**• This will change the direction of v, and change the direction of F towards more bending • How big is the circle? • Magnetic force is F = • Centripetal force is F = • We can combine to get r = mv/qB • Radius of orbit of charged particle in a uniform magnetic field**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 and they will come out separated by mass**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**Magnetic Field and Current**• We know that i = q/t and v = L/t (where L is the length of the wire) • So qv = iL, thus: F = BiL sin f • We can use the right hand rule to get the direction of the force • Use the direction of the current instead of v**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**Torque on Loop**• Since q = 90 and L = h, 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 t = iBA t = iBA sin q**General Loops**t = iBAN sin q • The torque is maximum when the loop is aligned with the field and zero when the field is at right angles to the loop (field goes straight through loop) • 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**Next Time**• Read 29.1-29.4 • Problems: Ch 28, P: 22, 36, 67, Ch 29, P: 1, 27 • Test 2 next Friday**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? • Right • Left • Up • Down • Right at you**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? • Right • Left • Up • Down • Right at you**A beam of electrons is pointing right at you. What**direction would a magnetic field have to have to produce no deflection? • Right • Left • Up • Down • Right at you