Magnetic Force
Physics 102Professor Lee
CarknerLecture 18
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 [(1.7X10-14)/((1.6X10-19)(3X105)
(0.5))] = v vector points 45 west of north, which is
pointed northwest, so electron was fired from southeast
Electron in B Field
vB
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)
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) RightB) LeftC) UpD) DownE) 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) RightB) LeftC) UpD) DownE) 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) RightB) LeftC) UpD) DownE) Right at you
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
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
Circular Motion If the particle moves at right angles to the field the
force vector will cause the path to bend
The particle will move in a circle How big is the circle?
Magnetic force is F = Centripetal force is F =
We can combine to getr = 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 they will
come out separated by mass
Today’s PAL
How long would it take an electron to complete one circular orbit around a 1 G magnetic field?
Helical Motion If the initial velocity is not completely perpendicular
to the field, instead of a circle you get a spiral or helix Charged particles will spiral around magnetic field
lines
For example, if the lines begin and end at a pole
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
Loop of Current
Torque on Loop For a loop of width w and height h, force is F = BIL sin
for each long side Since = 90 and L = h,
The torque is the force times the moment arm
(distance to the center), which is w/2 Total torque = but hw is the area of the loop, A
If the field is at angle to the loop then
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
Can harness the spin to do work Called a motor
Next Time
Read 20.7-20.8 Homework: Ch 20, P 4, 17, 38, 49 Exam #2 Friday