Magnetic Force Physics 102 Professor Lee Carkner Lecture 17

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 [(1.7X )/((1.6X )(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

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)

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

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

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)

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

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

Solar Wind Particles in Earth’s Magnetic Field

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

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

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

Torque on Loop

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 

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

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