Lecture 9/26 Chapter 22 Flashcards
QUICK QUIZ
At the Fermilab accelerator in Weston, Illinois, singlycharged ions with momentum 4.8 × 10−16 kg⋅m/s are held in
a circular orbit of radius 1 km by an upward magnetic field.
What B-field must be used to maintain the ions in this
orbit? (qion = 1.6 × 10−19 C)
3 T
Mass Spectrometer
An instrument for separating and
identifying atoms and molecules
by mass.
It relies on magnetic forces on
charged particles.
R=?
R=(mv) / (|q|B2)
or
R=mv / eB
v=?
v=B/B1
Magnetic Force Exerted on
a Current-Carrying Wire
Force on Current Carrying Conductor
The direction of the force is given by right hand rule #1
Force on a Wire
o The blue x’s indicate the magnetic field is directed into the page
o The x represents the tail of the arrow
o Blue dots would be used to represent the field directed out of the page
o The * represents the head of the arrow
o In this case, there is no current, so there is no force
Force on a Wire, equation
F = B I ℓ sin θ
o The magnetic force is exerted on each
moving charge in the wire
o The total force is the sum of all the
magnetic forces on all the individual
charges producing the current
o θ is the angle between and the direction of
I
o The direction is found by the right hand rule,
placing your fingers in the direction of I
instead of
B
r
v
QUICK QUIZ
A copper wire of length 25 cm is in a magnetic
field of 0.20 T. If it has a mass of 10 g, what is the minimum current through the wire that would cause a magnetic force equal to its weight?
2.0 A
Torque on a Current Loop
torque=NBIAsinθ
o Applies to any shape loop
o N is the number of turns in the coil
o Torque has a maximum value of NBIA
o When θ = 90°
o Torque is zero when the field is perpendicular to the plane of the loop
With Magnetic Moments, µ = NIA,
τ = µB sinθ
Electric Motor
o An electric motor converts electrical energy to mechanical energy
o The mechanical energy is in the form of rotational kinetic energy
o An electric motor consists of a rigid current-carrying loop that rotates when placed in a magnetic field
o To provide continuous rotation in one direction, the current in the loop must periodically reverse
o In ac motors, this reversal naturally occurs
o In dc motors, a split-ring commutator and brushes are used
o Actual motors would contain many current loops and commutators
QUICK QUIZ
A rectangular coil (0.20 m × 0.80 m) has 200 turns and
is in a uniform magnetic field of 0.30 T. If the
orientation of the coil is varied through all possible
positions, the maximum torque on the coil by magnetic
forces is 0.080 N⋅m. What is the current in the coil?
8.3 mA
Electric Currents &
Magnetic Fields
o A current-carrying wire produces a magnetic
field
o The compass needle deflects in directions
tangent to the circle
o The compass needle points in the direction of
the magnetic field produced by the current
o 1777 – 1851
o Best known for observing
that a compass needle
deflects when placed
near a wire carrying a
current
o First evidence of a
connection between
electric and
magnetic
phenomena
Direction of the Field of a
Long Straight Wire
o Right Hand Rule #2
o Grasp the wire
in your right
hand
o Point your
thumb in the
direction of the
current
o Your fingers will
curl in the
direction of the
field
Magnitude of the Field of a
Long Straight Wire with equation
o The magnitude of the field at a
distance r from a wire carrying a
current of I is
o µo = 4 π x 10-7 T.
m / A
o µo is called the permeability of free
space
B=(µoI)/(2πr)
QUICK QUIZ
A high-voltage power line 20 m above the
ground carries a current of 2 000 A. What is the
magnetic field due to the current directly
underneath the power line? (µ0 = 4π × 10−7 T⋅m/A)
20 µ T
