Download TOPIC 6: Fields and Forces

TOPIC 6.3: Magnetic
Fields and Forces
These notes were typed in association with Physics for use
with the IB Diploma Programme by Michael Dickinson
6.3 Magnetic Force and Field
6.3 Introduction.
We’ve already studied electric
fields and seen that they exist in
a region of space surrounding
an electric charge
This idea can be applied to
magnetism.
If iron filings are sprinkled on
top of a bar magnet, they will
show a pattern which traces the
lines of magnetic force around
the magnet.
6.3 Magnetic Force and Field
6.3 Introduction.
The earth behaves like a massive
magnet.
The south pole of the magnet at
the geographic north pole and
visa versa.
When a compass is positioned
anywhere within the Earth’s
magnetic field, the needle will
orientate itself along the Earth’s
magnetic field with it’s magnetic
north pole directed towards the
Earth’s geographic north pole.
6.3 Magnetic Force and Field
6.3.1 State that moving charges give rise to magnetic fields.
6.3.2 Draw magnetic field patterns due to currents.
When an electrical current flows in a piece of wire then a
magnetic field is produced around the wire.
We can correctly predict the direction of the magnetic field using
the “right hand grip rule”
6.3 Magnetic Force and Field
The thumb points to the current
The fingers show the direction of circular magnetic field.
The space between the field lines increase with distance from
the wire. Meaning a weaker field the further away.
6.3 Magnetic Force and Field
A solenoid is a long wire wrapped around a metal core which
produces a magnetic field when electric current is passed through
it. They are important because they create controlled magnetic
fields and can be used to convert energy into motion.
The fingers point in the direction of the current. The thumb
points in the direction of the magnetic field lines.
6.3 Magnetic Force and Field
6.3.3 Determine the direction of the force on a current-carrying
conductor in a magnetic field.
When a current-carrying wire is placed in a magnetic field a
magnetic force is produced. This usually causes either the magnet
or conductor to move.
The force will be perpendicular to the current and the magnetic
field.
We use “Fleming’s left hand rule”
6.3 Magnetic Force and Field
6.3.3 Determine the direction of the force on a current-carrying
conductor in a magnetic field.
This acronym might help: TFC
HAND
WIRE/MAGNET
Thumb
Thrust (force)
Fore finger
Field (magnetic)
Center finger
Current
6.3 Magnetic Force and Field
6.3.3 Determine the direction of the force on a current-carrying
conductor in a magnetic field.
Look at the diagram and identify the direction of the Fmag
Answer: Down
6.3 Magnetic Force and Field
6.3.3 Determine the direction of the force on a current-carrying
conductor in a magnetic field.
Drawing 3-D sketches can get confusing some times, so there is a
convention used. Consider a dart or arrow moving away from
you. You would see its tail end. If the dart was moving toward you
, you would see its tip.
6.3 Magnetic Force and Field
6.3.3 Determine the direction of the force on a current-carrying
conductor in a magnetic field.
That means the picture from earlier could be drawn like this.
6.3 Magnetic Force and Field
6.3.3 Determine the direction of the force on a current-carrying
conductor in a magnetic field.
The size of the magnetic force, Fmag, is proportional to the
strength of the magnetic field, B, the size of the current, I, and
the length of the wire (that is in the magnetic field), L.
IB Formula
F = BILsinθ
“sin θ” takes in account for the cases where the conductor and
the magnetic field are not perpendicular. Normally when they are
perpendicular, the angle between them is 90º and the sinθ
disappears.
6.3 Magnetic Force and Field
6.3.4 Determine the direction of the force on a charge moving in a
magnetic field.
When a charged particle moves in a magnetic field it will feel a
force. Current is a moving charge.
Conventional current is in the opposite direction to the flow of
electric charge.
6.3 Magnetic Force and Field
6.3.4 Determine the direction of
the force on a charge moving in a
magnetic field.
When a charge enters the
magnetic field it will feel a
force.
This force causes its direction
to change. As the direction of
motion changes so does the
force and it creates a circular
motion.
Let’s look at this diagram
starting at the top.
6.3 Magnetic Force and Field
6.3.4 Determine the direction of the force on a charge moving in a
magnetic field.
The size of the magnetic force, Fmag, is proportional to the
strength of the magnetic field, B, the velocity of the charge, v, and
the size of the charge, q.
IB Equation
F = qvBsinθ
6.3 Magnetic Force and Field
6.3.5 Define the magnitude and direction of a magnetic field.
Magnetic field strength, B, is measuered in Tesla, T. It is a vector
quantity, so if two magnetic fields interact, vector addition must
be used to calculate the resulting magnetic field.
We can combine the previous two equations and get the following
one.
IB Equation
F = BILsinθ
Permeability of free space = μ0 = 4π x 10-7 m/A
6.3 Magnetic Force and Field
6.3.6 Solve problems involving magnetic forces, fields and currents.
Practice 13
A piece of copper wire is held perpendicular to a magnetic field
of strength 0.25 Teslas. The length of the conductor within the
field is 10cm. If a current of 8 Amps is allowed to flow in the
wire, what is the force on the wire?
Answer: 0.2 N
6.3 Magnetic Force and Field
6.3.6 Solve problems involving magnetic forces, fields and currents.
Practice 14
The same piece of wire is now tilted so that it makes an angle of
30º to the magnetic field. What is now the force on the wire?
Answer: 0.1 N
6.3 Magnetic Force and Field
6.3.6 Solve problems involving magnetic forces, fields and currents.
Practice 15
An electron moves perpendicular to a magnetic field of strength
200µT. As it enters the field it is seen to move through a circular
path of radius 20cm. Calculate the speed of the electron.
***Hint: Since the electron moves in a circular path, it undergoes
centripetal acceleration and feels a centripetal force. This force
comes from the magnetic force.
Answer: 7.025 x 106 m/s