Download Goal: To understand Electro-magnetic fields

Goal: To understand Electromagnetic fields
Objectives:
1) To learn about Magnetic Fields
2) To be able to calculate the magnitude of
Magnetic Forces
3) To know how to use the Right Hand Rule
to get the direction of the magnetic force
4) To understand Motions of particles in a
Magnetic field
5) To learn about Cyclotrons
Magnetic Fields
• Just like with electric fields and
gravitational fields, magnetic fields are an
indicator of the magnetic topography of the
region.
• One example to illustrate this is the
magnetic dipole or bar magnet.
Bar magnets
• All have 2 ends, North and South
• This is like + and – for charges.
• This creates a field where charges for from
the north pole to the south pole just like
they went from + charge (high potential) to
– (low potential)
Magnetic Field
Lines
• Much like we had electric field lines we
have magnetic field lines.
• These are the lines which charges would
follow (sort of).
• These are the lines that charges or
magnetic materials would follow
Earth’s magnetic field (NASA)
Magnetic Force
• The magnetic force is very complicated.
• With electric fields the force is towards
charges usually.
• However, with magnetic forces, the force
is PERPENDICULAR to the magnetic
field.
• But before we examine that lets look at the
equation…
Magnetic Force Equation
• F=qVXB
• But V X B isn’t normal multiplication because V
and B are vectors.
• Turns out if V and B are in the same direction
(the angle between them is 0), then V X B are 0.
• Conversely if the angle is 90 degrees then you
just multiply as normal.
• So, F = qvBsin(θ) where θ is the angle between
the vectors v and B.
Okay first an example for the
MAGNITUDE of the force
• For most of what we will do velocity and B
will be perpendicular.
• Lets assume that to be true here.
• If the charge is 4C, the velocity is 200 m/s,
and B is 0.1 Tessla (T) then what is the
magnitude of the force?
Okay first an example for the
MAGNITUDE of the force
• For most of what we will do velocity and B
will be perpendicular.
• Lets assume that to be true here.
• If the charge is 4C, the velocity is 200 m/s,
and B is 0.1 Tessla (T) then what is the
magnitude of the force?
• F = qvBsin(θ) = qvB
• F = (done on board)
Direction of the force
• But what about the direction the force?
• Is it in the direction of the velocity or the
magnetic field?
Direction of the force
• But what about the direction the force?
• Is it in the direction of the velocity or the
magnetic field?
• NEITHER!
• The force is in the 3rd dimension!
• That is the force is perpendicular to both
the velocity and the magnetic field (told
you it was complicated).
Right Hand Rule
• To find the direction of the force we use
the right hand rule (left hand for a negative
charge).
• A=BXC
• A is the thumb.
• B index finger and C is the middle finger
Right Hand Rule
• To find the direction of the force we use the right
hand rule (left hand for a negative charge).
• A = B X C (F = q VXB)
• A is the thumb.
• B index finger and C is the middle finger.
• Lets try one:
• The velocity is in the +y direction and the
magnetic field is in the +x direction.
• What is the direction of the force?
Okay now lets put it all together!
• A +2C charge is moving in the –y direction
at a velocity of 40 m/s.
• If the magnetic field is 0.2 T in the +z
direction then what is the magnitude and
direction of the force?
One more
• A charge of 3C moving at 5 m/s in the +Z
direction experiences a force of 6 N in the
–Y direction.
• What is the magnitude and direction of the
magnetic field?
Motions in an electric field
• Now that we know what the force is, what
will the motion be like if the magnetic field
is constant?
• Hint: how does the force change with time
as the direction of the velocity of the
charge changes?
Motions in an electric field
• Now that we know what the force is, what will
the motion be like if the magnetic field is
constant?
• The charge will move in a circle!
• The force changes the direction of the velocity.
• However this changes the direction of the force.
• So, the charge will move in a circle
perpendicular to the magnetic field (around the
field lines).
• Any motion the particle has in the direction OF
the field will be constant (no force).
Cyclotrons
• A device which accelerates particles is
called a cyclotron.
• This is used mostly for protons (electrons
would just go in the opposite direction).
• This uses the fact that the radius of the
circle that a proton will move in just
depends on its velocity and the magnetic
field.
Centrifugal motion
• Remember in P218 that a = v2/r for circular
motions.
• Since a = F/m, then a = qvB / m = v2/r
• So, r = mv / qB and v = qBr / m
• Would do an example, but we are out of
time.
Conclusion
• We have learned what magnetic fields are and
why they are very important.
• We have learned that the magnitude of the force
is qvB and is perpendicular to either v or B.
• We learned how to use the Right Hand Rule to
find the direction of the force, velocity, or
magnetic field.
• In a constant B field charges move in circles.
• We can use this to create a cyclotron.