Duke Physics Magnetic Forces
Magnetic Forces on Currents
Introduction
When a charged particle moves in a magnetic field, there is force on the charge, F = qv × B, which is
called Lorentz force. For a comparison, the electric force on a charge in an electric field is Fe = q E.
The electric force is along the field direction, while the magnetic force is perpendicular to both v &
or in other words perpendicular to the plane formed by v × B.
B This is a consequence of the cross
product. The magnitude of the force is qvB sin(θ), where θ is the angle between v & B. In other
words, the force is the maximum (minimum) when the angle is 90 (0) degrees. One way to find the
direction of the magnetic force is to use the right-hand rule (recall the torque calculation, τ = r × F ).
To use the right-hand rule, it is important to match the tails of the two vectors.
When a charge free to move en-
ters a region of uniform magnetic
field, it makes a circular motion,
and the radius R of the circle
can be calculated by equating the
magnetic force to the centripetal
force (left picture below), qvB =
(mv2 )/R, or R = mv/qB. Here
m is the mass of the particle. The
right picture shown is from a de-
tector called a bubble chamber inside uniform magnetic field, which can track charged particles. The
track curvature is related to the momentum and charge of the particle. For example, straighter tracks
have higher momenta, and the tracks curving up have the opposite charge compared to the ones curv-
ing down. The spiral tracks are likely electrons or positrons. The radius decreases because as they
circle, they lose energy (velocity decreases) due to the interaction with the bubble chamber material.
Another application of the Lorentz force is the mass spec-
trometer, which separates particles according to their mass
(figure below). The particles with different masses but same
velocity are sent to a region of uniform magnetic field, and
depending on their masses, they end up at different loca-
tions.
Since the current is the movement of charges, it is not dif-
ficult to extend the magnetic force on a charge to a current
carrying wire by replacing qv with i dl. i is the current in
the wireR& dl is a small wire segment. Then dF = idl × B,
or F = i dl × B. The integral is normally evaluated nu-
merically except a few simple cases. For example, if the wire is straight in a uniform magnetic field,
then the integral becomes F = iL × B,
where L is the length of the wire. The magnitude of the force
is iLB sin(θ) where θ is the angle between the wire and magnetic field.
, Preliminary exercise
Time to start thinking about magnetic force and its direction in a field. Answer the following:
• The following figures show the current carrying wire segments (black lines) in B field. Find and
draw the direction of the force for each one. Check the solution among yourselves.
Equipment
A stand at your table holds a wooden rod supporting a thick brass wire in the shape of a rectangular
”U”. Sockets allow connection of the U to a power supply, using banana cables. A sensitive scale
holds a plastic platform that houses two rare-earth magnets. The magnets face each other to create
a uniform B-field between them. If the wire U is placed exactly between the magnets, then current
flowing in the U can exert a force on the magnets and, by extension, on the scale. An elevator platform
will let you adjust the height of the wire U.
Magnet platform. The plastic magnet platform can be
rotated and is marked with an angular scale around the
perimeter (the finest increments are spaced 2◦ ). For Exper-
iment 1 it will be important to ensure the current travels
at 90◦ to the B-field—not the magnet faces!
The Scale. The scale has 0.001 gram sensitivity. Level
it by adjusting the feet so the bubble indicator is in the
center. Zero it with the magnet platform sitting on top.
Note: elbows on your table can affect your data! Do not
turn off the scale. It is warmed up and ready to go—and
should be left turned on all day. You will see fluctuations
in the reading. This will indicate the level of uncertainty
you should estimate for your data points.
Figure 1: The magnet platform and the B
Power supply in current mode. You will use your power
supply in current mode. Adjust the voltage knob about field between the flat magnets.
halfway and leave it. The current adjust knob will now
set the current through the U-shaped wire. Your supply is capable of supplying 0-10 Amperes. We
will use at most 5A today, but this can heat your wires up too much if left on for a long time! (5-10
minutes for data taking should be fine.)
For safety, switch off your supply when you are not taking data!
Your goal today: To measure (as described in the instructions below) the force on a current placed
in the magnetic field between this magnet, and answer questions related to this physical phenomenon.
Magnetic Forces on Currents
Introduction
When a charged particle moves in a magnetic field, there is force on the charge, F = qv × B, which is
called Lorentz force. For a comparison, the electric force on a charge in an electric field is Fe = q E.
The electric force is along the field direction, while the magnetic force is perpendicular to both v &
or in other words perpendicular to the plane formed by v × B.
B This is a consequence of the cross
product. The magnitude of the force is qvB sin(θ), where θ is the angle between v & B. In other
words, the force is the maximum (minimum) when the angle is 90 (0) degrees. One way to find the
direction of the magnetic force is to use the right-hand rule (recall the torque calculation, τ = r × F ).
To use the right-hand rule, it is important to match the tails of the two vectors.
When a charge free to move en-
ters a region of uniform magnetic
field, it makes a circular motion,
and the radius R of the circle
can be calculated by equating the
magnetic force to the centripetal
force (left picture below), qvB =
(mv2 )/R, or R = mv/qB. Here
m is the mass of the particle. The
right picture shown is from a de-
tector called a bubble chamber inside uniform magnetic field, which can track charged particles. The
track curvature is related to the momentum and charge of the particle. For example, straighter tracks
have higher momenta, and the tracks curving up have the opposite charge compared to the ones curv-
ing down. The spiral tracks are likely electrons or positrons. The radius decreases because as they
circle, they lose energy (velocity decreases) due to the interaction with the bubble chamber material.
Another application of the Lorentz force is the mass spec-
trometer, which separates particles according to their mass
(figure below). The particles with different masses but same
velocity are sent to a region of uniform magnetic field, and
depending on their masses, they end up at different loca-
tions.
Since the current is the movement of charges, it is not dif-
ficult to extend the magnetic force on a charge to a current
carrying wire by replacing qv with i dl. i is the current in
the wireR& dl is a small wire segment. Then dF = idl × B,
or F = i dl × B. The integral is normally evaluated nu-
merically except a few simple cases. For example, if the wire is straight in a uniform magnetic field,
then the integral becomes F = iL × B,
where L is the length of the wire. The magnitude of the force
is iLB sin(θ) where θ is the angle between the wire and magnetic field.
, Preliminary exercise
Time to start thinking about magnetic force and its direction in a field. Answer the following:
• The following figures show the current carrying wire segments (black lines) in B field. Find and
draw the direction of the force for each one. Check the solution among yourselves.
Equipment
A stand at your table holds a wooden rod supporting a thick brass wire in the shape of a rectangular
”U”. Sockets allow connection of the U to a power supply, using banana cables. A sensitive scale
holds a plastic platform that houses two rare-earth magnets. The magnets face each other to create
a uniform B-field between them. If the wire U is placed exactly between the magnets, then current
flowing in the U can exert a force on the magnets and, by extension, on the scale. An elevator platform
will let you adjust the height of the wire U.
Magnet platform. The plastic magnet platform can be
rotated and is marked with an angular scale around the
perimeter (the finest increments are spaced 2◦ ). For Exper-
iment 1 it will be important to ensure the current travels
at 90◦ to the B-field—not the magnet faces!
The Scale. The scale has 0.001 gram sensitivity. Level
it by adjusting the feet so the bubble indicator is in the
center. Zero it with the magnet platform sitting on top.
Note: elbows on your table can affect your data! Do not
turn off the scale. It is warmed up and ready to go—and
should be left turned on all day. You will see fluctuations
in the reading. This will indicate the level of uncertainty
you should estimate for your data points.
Figure 1: The magnet platform and the B
Power supply in current mode. You will use your power
supply in current mode. Adjust the voltage knob about field between the flat magnets.
halfway and leave it. The current adjust knob will now
set the current through the U-shaped wire. Your supply is capable of supplying 0-10 Amperes. We
will use at most 5A today, but this can heat your wires up too much if left on for a long time! (5-10
minutes for data taking should be fine.)
For safety, switch off your supply when you are not taking data!
Your goal today: To measure (as described in the instructions below) the force on a current placed
in the magnetic field between this magnet, and answer questions related to this physical phenomenon.
