Download Current in a Magnetic Field * Learning Outcomes

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Current in a Magnetic Field – Learning
Outcomes
 Discuss the force on a current-carrying conductor in a
magnetic field.
 Demonstrate this force.
 Solve problems about this force.
 Discuss applications of this force.
 Define magnetic flux density.
 Discuss the force between currents.
 HL: Define the ampere.
 HL: Derive 𝐹 = 𝑞𝑣𝐵
 Solve problems about magnetic flux density.
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Force on a Current-Carrying Conductor
 Recall a current-carrying conductor has a magnetic
field around it.
 This field will interact with other nearby magnetic fields.
 This results in a force on the conductor.
 The size and direction of the force depends on the
nature of the two fields.
 The force is always:
 perpendicular to the current,
 perpendicular to the magnetic field.
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To Demonstrate the Force on a CurrentCarrying Conductor in a Magnetic Field
1. Set up a strip of tin foil between the north and south
poles of a magnet (or two magnets).
2. Note no deflection on the foil.
3. Pass a current through the foil.
4. The foil will move towards one of the poles, depending
on which way the current flows.
5. The foil must be experiencing a force due to the
external magnetic field.
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Uses of this Force
 This force is the basis for a number of electronic devices:
 Electric motor
 Moving coil loudspeaker
 Various moving coil meters (voltmeter, ammeter etc.)
 The jist is these devices respond to the size of the current
being passed through them.
 More detail on these in the applied electricity option
(we probably won’t do this).
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Fleming’s Left-Hand Rule
 If the thumb, index finger, and
middle finger of the left hand
are held at right angles to
each other; with the index
finger pointing in the direction
of the magnetic field and
middle finger pointing in the
direction of the current, the
thumb will point in the
direction of the force.
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Fleming’s Left-Hand Rule
 e.g. the diagram shows a current-carrying wire in a
magnetic field. In which direction is the force on the
wire?
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Magnetic Flux Density
 The strength of a magnetic field is given by its magnetic
flux density.
 The magnetic flux density, B at a point in a magnetic
field is a vector whose magnitude is equal to the force
per unit current per unit length that would be
experienced by a conductor at right angles to the field
at that point and whose direction is the direction of the
force on a north pole placed at that point.
 Formula: 𝐵 =
𝐹
𝐼𝑙
 B = magnetic flux density, F = force, I = current, l = length.
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Magnetic Flux Density
 The unit of magnetic flux density is the tesla, T.
 The magnetic flux density at a point is 1 tesla if a
conductor of length 1 m carrying a current of 1 A
experiences a force of 1 N when placed perpendicular
to the field.
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Force on a Current-Carrying Conductor
 Rearranging this formula gives:
 𝐹 = 𝐵𝐼𝑙
 This tells us the force is:
 proportional to the magnetic flux density,
 proportional to the current,
 proportional to the length of the conductor.
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Force on a Current-Carrying Conductor
 e.g. A straight piece of wire of length 3 m carrying a
current of 2 A experiences a force of 12 N when placed
perpendicular to a uniform magnetic field. Calculate
the value of the magnetic flux density.
 e.g. A straight piece of wire carrying a current of 4 A is
placed at an angle of 30o to a magnetic field of flux
density 2 T. The wire is 2 m long. What is the magnitude
and direction of the force on the wire?
Force on a Current-Carrying Conductor
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 e.g. The loop shown is free to
rotate about its axis.
i.
Find the magnitude and
direction of the force
acting on each part of the
loop.
ii.
Find the moment of the
force about the axis.
iii. What happens to the
moment as the loop
rotates?
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D.C. Motors
 Consider a loop that is free to rotate in a magnetic field.
 What is the direction of force on each part of the loop?
 What is the effect on the loop?
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D.C. Motors
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D.C. Motors
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Force Between Wires
 The force experienced by
these wires is:
A. both left
B. both right
C. attractive
D. repulsive
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Force Between Wires
 The force experienced by
these wires is:
A. both left
B. both right
C. attractive
D. repulsive
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The Ampere
 From this force between wires, we get the definition of
the ampere:
 The ampere is that constant current, which, if
maintained between two straight, parallel conductors of
infinite length and negligible cross-section, kept 1 metre
apart in a vacuum will exert a force of 2 × 10−7 newtons
per metre length of the other.
 As the ampere is a fundamental SI unit, we define the
coulomb based on it:
 The coulomb is the amount of charge that passes any
point in a circuit when a current of 1 ampere flows for 1
second.
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Force on a Charge in a Magnetic Field
 Just as current-carrying wires generate a magnetic field
and are affected by external fields, charges moving
without a wire will also exhibit this.
 e.g. cathode rays, thermionic emissions, photoelectric
emissions, ions in electrolyte solutions.
 We will look at each of these devices in turn in other
sections of the course.
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Force on a Charge in a Magnetic Field
 What direction is the force on this stream of electrons?
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Force on a Charge in a Magnetic Field
 Derive: 𝐹 = 𝑞𝑣𝐵
 Consider a current-carrying conductor of length 𝑙 with
current 𝐼.
 The flowing charges are size 𝑞 and have velocity 𝑣.
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Force on a Charge in a Magnetic Field
𝑞
𝑡
𝑙
=
𝑡
𝐼 =
(by definition)
𝑣
⇒ 𝑙 = 𝑣𝑡
 Substituting into 𝐹 = 𝐵𝐼𝑙 gives:
𝐹 =𝐵
𝑞
𝑡
𝑣𝑡 = 𝑞𝑣𝐵
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Force on a Charge in a Magnetic Field
 Consider an electron moving with velocity v in a
magnetic field.
 In what direction is the force on the electron?
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Force on Charge in a Magnetic Field
 e.g. A charge of 2 C moves at a speed of 10 m s-1 at
right angles to a magnetic field of flux density 2 T. What is
the force on the charge?
 e.g. An electron of charge 1.6 × 10-19 C enters a uniform
magnetic field of flux density 2 T and moves at right
angles to the field. If the force on the electron is 2 × 10-8
N, calculate the speed of the electron.
 e.g. Prove that the period T of the circular orbit of an
electron of mass m and charge e when moving at
speed v perpendicular to a magnetic field of flux density
2𝜋𝑚
B is given by: 𝑇 =
𝐵𝑒