Physics 272
March 4
Spring 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html
Prof. Philip von Doetinchem
philipvd@hawaii.edu
Phys272 - Spring 14 - von Doetinchem - 1
Summary
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Example:
rectangular loop
in a uniform
magnetic field
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The total force
on the loop is
zero
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But the total torque is
generally not zero
0
µ
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Summary
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Summary
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Greatest torque when magnetic dipole moment and
magnetic field are perpendicular
Torque is zero when magnetic dipole moment and
magnetic field are (anti)parallel
Analogue to electric dipole moment and electric field
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Summary
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Conductor strip perpendicular to a magnetic field
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Magnetic force causes polarization effect in material
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Electric field between lower and upper side of strip builds
up
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Sources of magnetic fields
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2002
2009
Current carrying
coils (solenoids)
can produce
massive uniform
magnetic fields
← particle physics
experiment CMS
at CERN in
Geneva uses a
solenoid
Phys272 - Spring 14 - von Doetinchem - 6
Magnetic field of a moving charge
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How are magnetic fields created?
Permanent magnets and electric currents create
magnetic fields
Magnetic field exerts a force only on moving charge
Moving charges inside atoms feel magnetic forces,
but can also act as sources
Start simple: single point charge moving with a
constant velocity
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Magnetic field of a moving charge
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Similar approach to electric field with point charges
→ be careful similarities and differences exist
Magnetic field magnitude
2
is proportional to charge and 1/r ,
but the direction of magnetic field is not along the
line of the charge and the point of interest
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Vector magnetic field
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Moving charge: magnetic field lines
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Moving point charge has
electric field and magnetic field
Electric field lines point
radially inwards or outwards
Magnetic field lines are
circles around centered
on the line of the velocity
and lying in perpendicular
planes to this line
Ignore acceleration of
charges in bends of wires
because the drift velocity
in conductors is so small
→ stick to assumption of
constant velocity
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Forces between two moving protons
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Forces between two moving protons
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Forces between two moving protons
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Forces between two moving protons
Force the upper proton →
feels from the magnetic field of the lower proton (repulsive)
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Forces between two moving protons
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Two protons moving in the same direction.
Magnetic force on
the upper proton
from the magnetic
field of the lower
proton: attractive
Magnetic force on
the lower proton
from the magnetic
field of the upper
proton: attractive
Phys272 - Spring 14 - von Doetinchem - 15
Force between moving charges
http://www.youtube.com/watch?v=43AeuDvWc0k
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Moving in the same direction for likewise signed
charges creates an attractive force and moving in
the opposite direction creates a repulsive force
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Magnetic field of a current element
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Superposition principle works for magnetic fields as well:
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The total magnetic field caused by several moving charges is
the vector sum of the fields caused by the individual charges.
Use to find magnetic field produced by a current in a
conductor
Chop charge-carrying conductor in short segments:
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Magnetic field of a current element
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Charges travel at average drift velocity (random
motions cancel out):
Magnetic field of a current element (vector version):
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Magnetic field of a current element
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Law of Biot and Savart:
Important law to find the total magnetic field of at
any point in space due to the current in a complete
circuit
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Magnetic field calculations
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Make a representative sketch of the current element
Draw current element dl → does it point in the direction
of the current?
Draw the unit vector for the straight connection between
the current element and the point you are interested in
What is your target variable?
Use the superposition principle to find the total magnetic
field.
Are there any symmetries? Which magnetic field
components are zero?
Does your result make sense? For instance, is the
magnetic field larger or smaller if you are further away
from the current element?
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Magnetic field of a current segment
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Copper wire carries a
steady current of
125A to a electroplating
tank. What is the
magnetic field of 1.0cm
long segment in 1.2m
distance?
Phys272 - Spring 14 - von Doetinchem - 23
Magnetic field of a current segment
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Copper wire carries a
steady current of
125A to a electroplating
tank. What is the
magnetic field of 1.0cm
long segment in 1.2m
distance?
Phys272 - Spring 14 - von Doetinchem - 24
Magnetic field of a straight current-carrying conductor
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Straight conducting wires are found in essentially all
electric and electronic devices
Conductor of a certain length a curring a current I.
Find magnetic field along the x axis:
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Magnetic field of a straight current-carrying conductor
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Straight conducting wires are found in essentially all
electric and electronic devices
Conductor of a certain length a curring a current I.
Find magnetic field along the x axis:
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Magnetic field of a straight current-carrying conductor
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Axial symmetry around the y axis
→ magnetic field has the same magnitude on all
points around a circle centered on the conductor
and lying in a plane perpendicular to it
Magnetic field direction is always a tangent on the
circle
Magnetic field lines enclose the current and do not
have end points
Calculation analog to an infinite sheet of current in
the case of electric fields, but magnetic field lines
have a different shape
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Magnetic field of a single wire
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Long straight conductor carries 1.0A: at what
distance is the magnetic field 50µT (~strength of
Earth magnetic field)?
Magnetic fields produced by household appliances
are typically small
→ only in close proximity to the conductor the
magnetic field is roughly as strong as Earth's
magnetic field
→ falls of as 1/r
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Magnetic field of two wires
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Two wires carry current in opposite directions. How
does the magnetic field on x along the x axis?
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Magnetic field of two wires
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At larger distances the magnetic field from the 2wire setup falls of as 1/r2.
→ The magnetic field from 2 wires carrying current
in opposite directions falls of quicker than from a
single wire (1/r).
Useful effect to minimize the distortion from currentcarrying wires on other cables carrying information
In this regard: it can be important to run cables of
different types (e.g., cables carrying tiny analog
signals and power supply cables) at either larger
distances or perpendicular to each other
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