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   Straight line  When  =  Circle  When  =  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

Helical Motion

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    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 Wire

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

Loop of Current

Torque on Loop   Since  = 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  = iBA   = iBA sin 

Torque on Loop

General Loops   = iBAN sin    he 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  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? A)Right B)Left C)Up D)Down E)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? A)Right B)Left C)Up D)Down E)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? A)Right B)Left C)Up D)Down E)Right at you