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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
Magnetic Fields, Magnetic Forces, and Conductors
• The Hall Effect
• Magnetic Force on a Current-Carrying Conductor
• Torque on a Current Loop: Rectangular and General
• Ampere's Law: Magnetic Field Due to a Long Straight Wire
• Magnetic Force Between Two Parallel Conductors
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
The Hall Effect
• The Hall effect is the phenomenon in which a voltage difference (called the Hall
voltage) is produced across an electrical conductor that is transverse to the
conductor's electric current when a magnetic field perpendicular to the
conductor's current is applied.
• Moving charges in a wire will change trajectory in the presence of a magnetic
field, "bending" toward it. Thus, those charges accumulate on one face of the
material. On the other face, there is left an excess of opposite charge. Thus, an
electric potential is created.
Hall Effect for Electrons
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
• [Equation 1]is the formula for Hall voltage (VH). It is a factor of current (I), magnetic field (B),
thickness of the conductor plate (t), and charge carrier density (n) of the carrier electrons.
Equation 1
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
Magnetic Force on a Current-Carrying Conductor
• Magnetic force on current can be found by summing the magnetic force on each
of the individual charges that make this current.
Right Hand Rule
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
• For a wire exposed to a magnetic field,[Equation 2]describes the relationship between magnetic
force (F), current (I), length of wire (l), magnetic field (B), and angle between field and wire (θ).
Equation 2
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
• The direction of the magnetic force can be determined using the right hand rule, as in fig [[17951]].
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
Torque on a Current Loop: Rectangular and General
• [Equation 3]can be used to calculate torque ([Equation 4]) a loop of N turns and A area, carrying I
current feels in the presence of a magnetic field B.
Equation 3
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Torque on a Current Loop
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Equation 4
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
Torque on a Current Loop: Rectangular and General
• Although the forces acting upon the loop are equal and opposite, they both act to
rotate the loop in the same direction.
• Torque experienced is independent of the loop's shape. What matters is the area
of the loop.
Torque on a Current Loop
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
Ampere's Law: Magnetic Field Due to a Long Straight Wire
• Ampere's Law states that for a closed curve of length C, magnetic field (B) is related to current (IC):
[Equation 5]. In this equation, dl represents the differential of length of wire in the curved wire, and μ0
is the permeability of free space.
Equation 5
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Direction of magnetic field
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
Ampere's Law: Magnetic Field Due to a Long Straight Wire
• Ampere's Law can be related to the Biot-Savart law, which holds for a short, straight length of
conductor: [Equation 6]. In this equation, partial magnetic field (dB) is expressed as a function of
current for an infinitesimally small segment of wire (dl) at a point r distance away from the conductor.
Equation 6
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Direction of magnetic field
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
Ampere's Law: Magnetic Field Due to a Long Straight Wire
• After integrating, the direction of the magnetic field according to the Biot-Savart
Law can be determined using the right hand rule.
Direction of magnetic field
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
Magnetic Force Between Two Parallel Conductors
• The field (B1) that that current (I1) from a wire creates can be calculated as a function of current and
wire separation (r): [Equation 7] μ0 is a constant.
Equation 7
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Magnetic fields and force exerted by
parallel current-carrying wires.
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
Magnetic Force Between Two Parallel Conductors
• [Equation 8] describes the magnetic force felt by a pair of wires. If they are parallel the equation is
simplified as the sine function is 1.
Equation 8
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Magnetic fields and force exerted by
parallel current-carrying wires.
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Magnetism > Magnetic Fields, Magnetic Forces, and Conductors
Magnetic Force Between Two Parallel Conductors
• The force felt between two parallel conductive wires is used to define the
ampere—the standard unit of current.
Magnetic fields and force exerted by parallel
current-carrying wires.
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Appendix
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Magnetism
Key terms
• ampere A unit of electrical current; the standard base unit in the International System of Units. Abbreviation: amp. Symbol: A.
• current The time rate of flow of electric charge.
• drift velocity The average velocity of the free charges in a conductor.
• electric field A region of space around a charged particle, or between two voltages; it exerts a force on charged objects in its
vicinity.
• elementary charge The electric charge on a single proton.
• magnetic field A condition in the space around a magnet or electric current in which there is a detectable magnetic force, and
where two magnetic poles are present.
• magnetic field A condition in the space around a magnet or electric current in which there is a detectable magnetic force, and
where two magnetic poles are present.
• magnetic field A condition in the space around a magnet or electric current in which there is a detectable magnetic force, and
where two magnetic poles are present.
• torque A rotational or twisting effect of a force; (SI unit newton-meter or Nm; imperial unit foot-pound or ft-lb)
• transverse Not tangent, so that a nondegenerate angle is formed between the two things intersecting.
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Magnetism
Direction of magnetic field
The direction of the magnetic field can be determined by the right hand rule.
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Connexions. "Magnetic field due to current in straight wire." CC BY 3.0 http://cnx.org/content/m31103/latest/ View on Boundless.com
Magnetism
Torque on a Current Loop
Electrical energy from the current is converted to mechanical energy as the loop and shaft rotate, and this mechanical energy is then used to power
another device.
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Connexions. "Torque on a Current Loop: Motors and Meters." CC BY 3.0 http://cnx.org/content/m42380/latest/ View on Boundless.com
Magnetism
Hall Effect for Electrons
Initially, the electrons are attracted by the magnetic force and follow the curved arrow. Eventually, when electrons accumulate in excess on the left side
and are in deficit on the right, an electric field ξy is created. This force becomes strong enough to cancel out the magnetic force, so future electrons
follow a straight (rather than curved) path.
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Wikipedia. "Hall Effect Measurement Setup for Electrons." CC BY-SA http://en.wikipedia.org/wiki/File:Hall_Effect_Measurement_Setup_for_Electrons.png View on
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Magnetism
Varying torque on a charged loop in a magnetic field
Maximum torque occurs in (b), when is 90 degrees. Minimum torque is 0, and occurs in (c) when θ is 0 degrees. When loop rotates past =0, the torque
reverses (d).
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Connexions. "Torque on a Current Loop: Motors and Meters." CC BY 3.0 http://cnx.org/content/m42380/latest/ View on Boundless.com
Magnetism
Magnetic fields and force exerted by parallel current-carrying wires.
Currents I1 and I2 flow in the same direction, separated by a distance of r.
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Connexions. "Magnetic Force between Two Parallel Conductors." CC BY 3.0 http://cnx.org/content/m42386/latest/ View on Boundless.com
Magnetism
Right Hand Rule
Used to determine direction of magnetic force.
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Connexions. "Magnetic Force on a Current-Carrying Conductor." CC BY 3.0 http://cnx.org/content/m42398/latest/ View on Boundless.com
Magnetism
The Hall voltage is produced across an electrical conductor that is
transverse to the conductor's electric current when
A) a magnetic field parallel to the conductor's current is applied
B) a magnetic field perpendicular to the conductor's current is applied
C) an electric field perpendicular to the conductor's current is applied
D) an electric field parallel to the conductor's current is applied
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Magnetism
The Hall voltage is produced across an electrical conductor that is
transverse to the conductor's electric current when
A) a magnetic field parallel to the conductor's current is applied
B) a magnetic field perpendicular to the conductor's current is applied
C) an electric field perpendicular to the conductor's current is applied
D) an electric field parallel to the conductor's current is applied
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Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/
Magnetism
When an electrical wire is exposed to a magnet, the current in that
wire
A) is not affected by a magnetic field
B) experiences a force
C) does not experience a force
D) remains intake
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Magnetism
When an electrical wire is exposed to a magnet, the current in that
wire
A) is not affected by a magnetic field
B) experiences a force
C) does not experience a force
D) remains intake
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Magnetism
The torque on a loop of any shape exposed to a magnetic field (B)
can be calculated by:
A) , where N is the number of turns of area A, I is the carrying current,
and θ is the angle
B) , where N is the number of turns of area A, I is the carrying current,
and θ is the angle
C) , where N is the number of turns of area A, I is the carrying current,
and θ is the angle
D) , where N is the number of turns of area A, I is the carrying current,
and θ is the angle
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Magnetism
The torque on a loop of any shape exposed to a magnetic field (B)
can be calculated by:
A) , where N is the number of turns of area A, I is the carrying current,
and θ is the angle
B) , where N is the number of turns of area A, I is the carrying current,
and θ is the angle
C) , where N is the number of turns of area A, I is the carrying current,
and θ is the angle
D) , where N is the number of turns of area A, I is the carrying current,
and θ is the angle
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Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/
Magnetism
Attribution
• Connexions. "Magnetic Force on a Current-Carrying Conductor." CC BY 3.0 http://cnx.org/content/m42398/latest/
• Wiktionary. "magnetic field." CC BY-SA 3.0 http://en.wiktionary.org/wiki/magnetic+field
• Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//physics/definition/drift-velocity
• Connexions. "Magnetic Force between Two Parallel Conductors." CC BY 3.0 http://cnx.org/content/m42386/latest/
• Wiktionary. "magnetic field." CC BY-SA 3.0 http://en.wiktionary.org/wiki/magnetic+field
• Wiktionary. "current." CC BY-SA 3.0 http://en.wiktionary.org/wiki/current
• Wiktionary. "ampere." CC BY-SA 3.0 http://en.wiktionary.org/wiki/ampere
• Wiktionary. "torque." CC BY-SA 3.0 http://en.wiktionary.org/wiki/torque
• Connexions. "Torque on a Current Loop: Motors and Meters." CC BY 3.0 http://cnx.org/content/m42380/latest/
• Wikipedia. "Hall effect." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Hall_effect
• Wiktionary. "transverse." CC BY-SA 3.0 http://en.wiktionary.org/wiki/transverse
• Wiktionary. "elementary charge." CC BY-SA 3.0 http://en.wiktionary.org/wiki/elementary+charge
• Connexions. "Magnetic field due to current in straight wire." CC BY 3.0 http://cnx.org/content/m31103/latest/
• Connexions. "Ampere's law." CC BY 3.0 http://cnx.org/content/m31895/latest/
• Wikipedia. "Ampère's circuital law." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Amp%25C3%25A8re's_circuital_law
• Wikipedia. "Biot–Savart law." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Biot%25E2%2580%2593Savart_law
• Wiktionary. "magnetic field." CC BY-SA 3.0 http://en.wiktionary.org/wiki/magnetic+field
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Magnetism
• Wiktionary. "electric field." CC BY-SA 3.0 http://en.wiktionary.org/wiki/electric+field
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