Magnetism

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Magnetism

• Magnetism
• Updated 3/15/07

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Magnetism

• In this section we are going to learn about
  magnets and magnetism, how they relate to
  electric charges, and the associated forces and
  fields.
• Magnets
• Magnetic Fields
• Lorentz Force
• Particle Trajectory
• Force on Conductor
• Amperes Law

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Magnetism

• Electricity and magnetism are different aspects
  of the electromagnetic force.
• Electric charges have a plus or a minus charge.
  Unlike charges attract and like charges repel.
• Magnets have north and south poles. Again,
  unlike poles attract and like poles repel.

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Magnetism

• By convention, electric fields run from plus
  charge to minus.
• Magnetic Fields run from north to south.
• Poles of a magnet are the ends where objects are
  most strongly attracted.

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Magnetism

• Magnetic poles cannot be isolated
• If a permanent magnetic is cut in half, you will
  still have a north and a south pole on the cut
  pieces
• This differs from electric charges
• There is some theoretical basis for monopoles,
  but none have been detected

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Magnetism
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Magnetism

• Electrical currents (moving charges) cause
  magnetic fields and vice versa.
• One form of moving charge is an electron orbiting
  the nucleus of an atom. Thus the atom produces a
  magnetic field directed along the axis of the
  atom.
• The atomic magnets are called domains.

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Magnetism

• The internal magnetic fields of the atoms form
  magnetic domains.
• the atomic domains have an internal north and a
  south pole aligned on the atoms axis
• in some material, atomic domains are oriented in
  random directions. In other materials the atomic
  domains align with each other, creating a magnet.

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Magnetism
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Magnetism

• Differences between electric and magnetic fields
  include
• electric charges exist on their own, magnetic
  poles come in pairs.
• stationary magnets dont feel a force in an
  electric field
• stationary charges dont feel a force in a
  magnetic field.

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Magnetism

• Definitions
• flux the term used for a magnetic field. Flux
  lines are the same as field lines.
• The convention is for magnetic flux (field) lines
  to go from north to south poles.

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Magnetism
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Magnetism

• A compass can be used to show the direction of
  the magnetic field lines.

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Magnetism

• Earths Magnetic Field
• The earths north pole is actually a magnetic
  south pole, and is offset from the geographic
  pole by about 11 degrees.
• This means that the north pole of a compass
  magnet will generally point towards the
  geographic north pole.

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Magnetism

• Earths Magnetic Field
• The Earths magnetic field resembles a field that
  would be achieved by burying a huge bar magnet
  deep in the Earths interior

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Magnetism

• When moving through a magnetic field, a charged
  particle experiences a magnetic force. (Right
  Hand Rule)
• This force has a maximum value when the charge
  moves perpendicularly to the magnetic field lines
• This force is zero when the charge moves parallel
  to the field lines.

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Magnetism

• Experiments show that the direction of the
  magnetic force is always perpendicular to both v
  and B
• Fmax occurs when v is perpendicular to B
• F 0 when is v parallel to B

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Magnetism

• Right Hand Rule 1
• With an open hand, place your fingers in the
  direction of the magnetic field, B
• Extend your thumb in the direction of the charge
  movement or current flow, v or I
• Your palm points in the direction of the force F,
  on a positive charge
• Use your left hand for a negative charge or
  current flow.

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Magnetism

• Now we come to three important equations of
  electromagnetism
• The force on a charge moving in a uniform
  magnetic field.
• The force on a current carrying wire in a uniform
  magnetic field.
• The magnetic field created by a current carrying
  wire.

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Magnetism

• Force on a charge moving in a magnetic field
• F q v B sin ?
• where F Force in Newtons
• B Magnetic Field in Teslas
• q Charge in Coulombs
• v Velocity in meters per second
• ? Angle between velocity and field

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Magnetism

• Force on a current (wire) in a magnetic field
• F B I L sin ?
• where F Force in Newtons
• B Magnetic Field in Teslas
• I Current in Amps
• L Length of current in meters
• ? Angle between current and field

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• Force on a current (wire) in a magnetic field

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Magnetism

• Magnetic field created by a current (wire)
• B µ0 I
• ------------------------------
• 2pr
• where µ0 4p x 10-7 T m / A
• B Magnetic Field in Teslas
• I Current in Amps
• r Distance between wire and point

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Magnetism

• A current-carrying wire produces a magnetic field
• The compass needle deflects in directions tangent
  to the circle
• The compass needle points in the direction of the
  magnetic field produced by the current

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Magnetism

• Right Hand Rule 2
• Grasp the wire in your right hand.
• Point your thumb in the direction of the current.
• Your fingers will curl in the direction of the
  field.

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Magnetism

• Definitions
• ampere If two long, parallel wires 1 m apart
  carry the same current, and the magnetic force
  per unit length on each wire is 2 x 10-7 N/m,
  then the current is defined to be 1 A.
• coulomb If a conductor carries a steady current
  of 1 A, then the quantity of charge that flows
  through any cross section in 1 s is 1C.

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Magnetism

• Two Wires
• The force on wire 1 is due to the current in wire
  1 and the magnetic field produced by wire 2
• The force per unit length is

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Magnetism

• Current Loop
• The strength of a magnetic field B produced by a
  wire can be enhanced by forming the wire into a
  loop (or loops).
• All the ?x segments contribute to the field,
  increasing its strength

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Magnetism

• Current Loop Magnetic Field

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Magnetism

• Magnetic field created by a current loop
• With N loops in the coil, this becomes
• where µ0 4p x 10-7 T m / A
• B Magnetic Field in Teslas
• I Current in Amps
• R Radius of Loop
• N Number of Loops

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Magnetism

• Electric DC Motor
• An electric motor converts electrical energy to
  mechanical energy in the form of rotational KE
• An electric motor consists of a rigid
  current-carrying loop that rotates when placed in
  a magnetic field.

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Magnetism

• Solenoid
• If a long straight wire is bent into a coil of
  several closely spaced loops, the resulting
  device is called a solenoid
• It is also known as an electromagnet since it
  acts like a magnet only when it carries a current

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Magnetism

• Solenoid
• The field lines inside the solenoid are nearly
  parallel, uniformly spaced, and close together
• This indicates that the field inside the solenoid
  is nearly uniform and strong
• The exterior field is nonuniform, much weaker,
  and in the opposite direction to the field inside
  the solenoid

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Magnetism

• Solenoid
• The field lines of the solenoid resemble those of
  a bar magnet.

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Magnetism

• Solenoid
• The magnitude of the field inside a solenoid is
  constant at all points far from its ends. If the
  solenoid is long compared to its radius, we
  assume the field inside is uniform and outside is
  zero.
• B µo n I
• n is the number of turns per unit length
• n N / l

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Magnetism

• End of Magnetism