Download Magnetic Force on a Current

Nighttime exam?
 If we have the exam in the evening of July 3rd, we
would cancel class on July 5th and you get a long
weekend. Would you prefer to have a nighttime
exam on July 3rd rather than an in-class exam on
July 5th?
A.I’d prefer to have an evening exam on July 3rd
B.I’d prefer to have an in-class exam on July 5th
C.I cannot attend an evening exam (e.g. because of
work)
Survey
 We’ve covered a lot of material in a short period of
time. If we slow down, you will have to teach yourself
more from the book, but we can go into further depth
in class on the topics we do cover. How do you feel
about the pacing of the class?
A.Too slow. Speed up.
B.The pacing is good.
C.Too fast. Slow down.
Survey
 This is the first year I’ve used iClicker quizzes during
lecture. The quizzes are intended to encourage
discussion of the material and to understand how to
apply the physical principles. How helpful have the
quizzes been to your learning?
A.Not helpful at all.
B.Somewhat helpful.
C.Very helpful
Chapter 20
Magnetic Fields and Forces
Review
 Magnetic fields
 Are due to moving charges

Right-hand rule 1 (currents)
 Act similar to electric fields with important differences





Opposites attract, likes repel
Obey superposition principle
Field lines make loops from north to south poles
No magnetic mono-poles
Force is perpendicular to direction of field
Magnetic Field and Current
Loop
 Treat the loop as many
small pieces of wire
 Apply the right-hand
rule to find the field from
each piece of wire
 Applying superposition
gives the overall pattern
shown in fig. 20.9B
Section 20.1
Right-hand Rule 1
1
 What is the direction of
the magnetic field in
regions 1, 2 and 3?
 B1 and B3 are non-zero
I
2
 They would be zero if
these were two sheets
of current
I
3
Magnetic Forces & Bar Magnets
• To determine the total force on
the bar magnet, you must look
at the forces on each pole
• The total force is zero
• The total torque is non-zero
• The torque acts to align the bar
magnet along the magnetic field
Section 20.2
Magnetic Moment
 The bar magnet possesses a
magnetic moment
 The bar magnet acts similar to an
electric dipole
 The poles of the magnet act as a
“magnetic charge”
 The north pole of one magnet will
attract the south pole of another
magnet
 Unlike poles attract
 Like poles will repel
 Similar to electric charges
Section 20.2
Comparing Electric and
Magnetic Fields and Forces
 Similarities
 Behavior between poles/charges
 Behavior in field lines
 Relation to distance
 Differences
 North and south magnetic poles always occur in pairs

An isolated magnetic pole has never been found
 Magnetic fields do not terminate
 Magnetic force is perpendicular to motion of charge
Section 20.2
Force on Moving Charge
 Magnetic force acts on individual moving charges
 The force depends on the velocity of the charge

If the charge is not moving, there is no magnetic force
 If a positive charge, q, is moving with a given
velocity, v, in an external magnetic field, B, then the
magnitude of the force on the charge is
 The angle θ is the angle between the velocity and the
field
Section 20.3
Right Hand Rule 2
 Used to determine the direction of
the force on moving charges
 Point the figures of your right hand
in the direction of the velocity and
curl them in the direction of the field
 Your thumb points in the direction of
the force
Section 20.3
Motion of a Charged Particle
 A charged particle moves
parallel to the magnetic field
 The angle between the
velocity and the field is zero
 Therefore, the force is also
zero
 Since sin θ = 0
Section 20.3
Motion of a Charged Particle, 2
 A charged particle moves
perpendicular to the magnetic
field
 The angle between the velocity
and the field is 90o
 Therefore, the force is
 The particle will move in a circle
Section 20.3
Motion of a Charged Particle, 2
 The circle lies in the plane perpendicular to the
magnetic field lines
 The radius of the circle can be calculated from noting
there must be a centripetal force acting on the
particle
Section 20.3
Motion of a Charged Particle, 3
 A charged particle moves
neither parallel nor
perpendicular to the
magnetic field
 The angle between the
velocity and the field
varies
 The path of the particle is
helical
 The charged particle will
spiral around the
magnetic field lines
Section 20.3
Motion of a Charged Particle
 Mass spectrometer
 Ions with different masses will
travel in arcs with different radii
 Calculate charge to mass ratio
 Hall probe
 Force on different sign charges
creates potential difference
 Used to measure magnetic
fields
 Bubble chamber
 Used in particle physics
Section 20.6
Example: Bubble Chamber
 Used in particle physics to
investigate decay products
 What is the sign of the
charge?
 What is the relative mass?
Right-Hand Rule
 Right-hand Rule 1 gives
direction of Magnetic
Field due to current
 Right-hand Rule 2 gives
direction of Force on a
moving positive charge
Section 20.1
Magnetic Force on a Current
 An electric current is a collection of
moving charges
 Obeys magnetic force law
 From the equation of the force on a
moving charge, the force on a currentcarrying wire is
 The direction of the force is given by the
right-hand rule 2
Section 20.4
Ampère’s Law
 Ampère’s Law can be
used to calculate the
magnetic field when there
is symmetry
 Similar to Gauss’ Law for
electric fields
 Relates the magnetic field
along a path to the electric
current enclosed by the
path
Section 20.7
Ampère’s Law, cont.
 The magnetic field along a
closed path is related to the
current enclosed by that path
 μo is the permeability of free
space
 μo = 4 π x 10-7 T . m / A
 If B varies in magnitude or
direction along the path,
Ampère’s Law is not useful
Section 20.7
Magnetic Field of a Long Straight Wire
 Ampère’s Law can be used to
find the magnetic field near a
long, straight wire
 Choose a circular, closed path
 B|| is the same all along the path
 If the circular path has a radius
r, then the total path length is 2
πr
 Applying Ampère’s Law gives
μo I
B
2π r
Section 20.7
Example: Two Parallel Wires
 What is the force on
I
1
wire 1 due to wire 2?
 Is the force attractive or
r
L
repulsive?
2
I
Field from a Current Loop
 It is not possible to find
a simple path along
which the magnetic field
is constant
 Ampère’s Law cannot be
easily applied
 From other techniques,
μo I
B
2R
Section 20.7
Field Inside a Solenoid
 By stacking many loops close
together, the field along the
axis is much larger than for a
single loop
 A helical winding of wire is
called a solenoid
 More practical than stacking
single loops
 For a long solenoid, there is
practically no field outside
Section 20.7
Example: Long Solenoid
What is the magnetic
field, B, inside a “long”
solenoid?
Torque on a Current Loop
 A magnetic field can produce a torque on a current loop
 Assume a square loop with sides of length L carrying a
current I in a constant magnetic field
 The directions of the forces can be found from right-hand
rule 2
Section 20.5
Torque, cont.
 On two sides, the current is parallel or antiparallel to the field, so the
force is zero on those sides
 The forces on sides 1 and 3 are in opposite directions and produce a
torque on the loop
 When the angle between the loop and the field is θ, the torque is
τ = I L2 B sin θ
 For different shapes, this becomes
Section 20.5
τ = I A B sin θ
Magnetic Moment, μ
 For a current loop, the
magnetic moment, μ, is I A
 The direction of the magnetic
moment is either along the axis
of the bar magnet or
perpendicular to the current
loop
 The strength of the torque
depends on the magnitude of
the magnetic moment
 τ = μ B sin θ
Section 20.5
Electric Motor
 A magnetic field can produce a torque on a current loop
 If the loop is attached to a rotating shaft, an electric motor
is formed
 In a practical motor, a solenoid is used instead of a single
loop
 Additional set-up is needed to keep the shaft rotating
Section 20.10
Electric Generator
 Electric generators are closely related to motors
 A generator produces an electric current by rotating
a coil between the poles of the magnet
 A motor in reverse
Section 20.10