Download Physics Lecture #29

Wed. Feb. 11 – Physics Lecture #29
Magnetic Forces
1. Magnetic Forces on Charged Particles
2. Motion in Magnetic Fields
3. Magnetic Forces on Current-Carrying Conductors
Warm-Up, Discuss with Neighbors: A uniform magnetic field in this room
points from the floor towards the ceiling. What is the direction of the magnetic
force acting on the particles in the various situations below?
a) A motionless proton?
b) A proton moving towards the front of the room?
c) An electron moving towards the front of the room?
d) A neutron moving towards the front of the room?
e) A proton moving straight up toward the ceiling?
f)
An electron moving to the right?
g) A proton moving diagonally from the back right to the front left?
Example: A particle with charge q moves with speed v at an angle of 30
degrees North of East. It enters a region of space with uniform magnetic field B
directed at an angle of 10 degrees West of North. Determine the magnetic force
(magnitude and direction) acting on the particle when it enters the magnetic
field.
Example: Calculate the magnetic force acting on a particle
with charge q
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moving with velocity v  vx iˆ  vy ˆj  vz kˆ in a magnetic field B  By ˆj  Bz kˆ
ConceptCheck: An electron and a proton move
with the same velocity. They enter a region
that has a uniform magnetic field directed into
the page as shown. Which of the following
sketches best represents their paths? Neglect
their interactions with each other.
p
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e
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ConceptCheck: A charged particle is in a region of space with a uniform
magnetic field (no other fields are present). Which of the following describes a
possible path the charged particle can travel? (Put up as many cards as you
think possible.)
1. No motion
2. Straight line
3. Parabola
4. Circle
5. Helix
6. Square
Magnetic Forces and Circular Motion:
How do we determine the radius of any circular motion associated with
magnetic forces?
Magnetic Forces & Work:
A charged particle is in a region of space with a uniform magnetic field (no other
fields are present). What can we say about the change in kinetic energy of the
charged particle?
Example: Velocity Selector
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An electron travels with velocity v0 through a
region of uniform magnetic field B directed out
of the page as shown.
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The electron is moving in a straight line.
How do you know there must be another field present?
If the other field is a uniform electric field, what is its direction?
What is the magnitude of this electric field?
What happens if you send in a particle with charge +2e but the same velocity?
What happens if you send in an electron with a slower speed (but same
direction?)
Example: Wire in Field.
A conducting wire is in a uniform magnetic field directed
up as shown. Conventional current I flows in the wire
towards the left.
a) What is the direction of the magnetic force?
b) What is the magnitude of this magnetic force?
c) What if the wire were angled at 30 degrees with respect to horizontal?
d) Return to the original scenario. The actual charge carriers in this wire are
electrons, so the electron current flows in the wire towards the right. What is
the direction of the magnetic force?
e) We argued previously that magnetic forces do no work. How can the wire
start from rest and begin to move?
Example: Hall Effect.
A wire is held fixed in a uniform magnetic
field pointing into the page. The wire carries
current I going towards the right.
ConceptCheck: If the charge carriers were
positively charged, what would be the sign
of DVbottomtop = Vtop – Vbottom, the potential
difference between the top side and the
bottom side of the wire?
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1. DV > 0
2. DV = 0
3. DV < 0
4. Not enough info
What would be different if the charge carriers were negative instead of positive?
What is the potential difference between the top and bottom side of the wire?
Assume known distances.