Magnetic Forces

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Magnetic Forces
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Forces in Magnetism

• The existence of magnetic fields is known because
  of their affects on moving charges.
• What is magnetic force (FB)?
• How does it differ from electric force (FE)?
• What is known about the forces acting on charged
  bodies in motion through a magnetic field?
• Magnitude of the force is proportional to the
  component of the charges velocity that is
  perpendicular to the magnetic field.
• Direction of the force is perpendicular to the
  component of the charges velocity perpendicular
  to the magnetic field(B).

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Magnetic Force (Lorentz Force)

• FB qvB sin?
• Because the magnetic force is always
  perpendicular to the component of the charges
  velocity perpendicular to the magnetic field, it
  cannot change its speed.
• Force is maximum when the charge is moving
  perpendicular to the magnetic field (? 90?).
• The force is zero if the charges velocity is in
  the same direction as the magnetic field (?
  0?).
• Also, if the speed is not changing, KE will be
  constant as well.

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Example 1

• A positively charged particle traveling at 7.5 x
  105 meters per second enters a uniform magnetic
  field perpendicular to the lines of force. While
  in the 4.0 x 10-2 tesla magnetic field, a net
  force of 9.6 x 10-15 newton acts on the particle.
  What is the magnitude of the charge on the
  particle?

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What is the magnetic field (B)?

• The magnetic field is a force field just like
  electric and gravitational fields.
• It is a vector quantity.
• Hence, it has both magnitude and direction.
• Magnetic fields are similar to electric fields in
  that the field intensity is directly proportional
  to the force and inversely related to the charge.
• E FE/q
• B FB/(qv)
• Units for B Ns/Cm 1 Tesla

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Right Hand Rules

• Right hand rule is used to determine the
  relationship between the magnetic field, the
  velocity of a positively charged particle and the
  resulting force it experiences.

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Right Hand Rules
2
1
3
FB qv x B
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The Lorentz Force Equation RHR
FB qvB sin?

• What is the direction of force on the particle by
  the magnetic field?
• Right b. Left c. Up d. Down
• Into the page f. Out of the Page

Note Only the component of velocity
perpendicular to the magnetic field (v?sin?) will
contribute to the force.
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Right Hand Rule What is the Force?
What is the direction of the magnetic force on
the charge? a) Down b) Up c) Right
d)Left
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Right Hand Rule What is the Charge?

• Particle 1
• Positive
• Negative
• Neutral
• Particle 2
• Positive
• Negative
• Neutral
• Particle 3
• Positive
• Negative
• Neutral

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Right Hand Rule What is the Direction of B

• What is the direction of the magnetic field in
  each chamber?
• Up
• Down
• Left
• Right
• Into Page
• Out of Page

1
4
2
3

• What is the speed of the particle when it leaves
  chamber 4?
• v/2 b. -v
• v d. 2v

Since the magnetic force is always perpendicular
to the velocity, it cannot do any work and change
its KE.
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Example 2 Lorentz Force
Two protons are launched into a magnetic field
with the same speed as shown. What is the
difference in magnitude of the magnetic force on
each particle? a. F1 lt F2 b. F1 F2 c.
F1 gt F2
F qv x B qvBsin? Since the angle between B
and the particles is 90o in both cases, F1 F2.
How does the kinetic energy change once the
particle is in the B field? a. Increase b.
Decrease c. Stays the Same
Since the magnetic force is always perpendicular
to the velocity, it cannot do any work and change
its KE.
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Trajectory of a Charge in a Constant Magnetic
Field

• What path will a charge take when it enters a
  constant magnetic field with a velocity v as
  shown below?

• Since the force is always perpendicular to the v
  and B, the particle will travel in a circle
• Hence, the force is a centripetal force.

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Radius of Circular Orbit
What is the radius of the circular orbit?
Lorentz Force F qv x B Centripetal Acc ac
v2/R Newtons Second Law F mac qvB
mv2/R R mv/qB
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Example 2

• A particle with a charge of 5.0 x 10-6 C
  traveling at 7.5 x 105 meters per second enters a
  uniform magnetic field perpendicular to the lines
  of force. The particle then began to move in a
  circular path 0.30 meters in diameter due to a
  net force of 1.5 x 10-10 newtons. What is the
  mass of the particle?

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Earths Magnetosphere

• Magnetic field of Earths atmosphere protects us
  from charged particles streaming from Sun (solar
  wind)

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Aurora

• Charged particles can enter atmosphere at
  magnetic poles, causing an aurora

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Crossed Fields in the CRT

• How do we make a charged particle go straight if
  the magnetic field is going to make it go in
  circles?
• Use a velocity selector that incorporates the use
  of electric and magnetic fields.
• Applications for a velocity selector
• Cathode ray tubes (TV, Computer monitor)

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Crossed Fields

• E and B fields are balanced to control the
  trajectory of the charged particle.
• FB FE
• Velocity Selector
• qvB qE
• v E/B

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Force on a Current Carrying Wire
FB qv x B qvB sin? (1) Lets assume that
the charge ?q travels through the wire in time
?t. FB (?q)vBsin? When ?t is factored in, we
obtain FB (?q/?t)(v?t) Bsin? (2) Where
?q/?t I (current) v?t L (length of
wire) Equation (2) therefore reduces to FB
ILB sin?
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Examples 2 3

• A wire 0.30 m long carrying a current of 9.0 A is
  at right angles to a uniform magnetic field. The
  force on the wire is 0.40 N. What is the strength
  of the magnetic field?

• A wire 650 m long is in a 0.46 T magnetic field.
  A 1.8 N force acts on the wire. What current is
  in the wire?

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Torque on a Current Carrying Coil (Electric
Motors/Galv.)
? Fr
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Torque on a Current Carrying Coil (cont.)
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Torque on a Current Carrying Coil (cont.)

• At zero torque, the magnetic field of the loop of
  current carrying wire is aligned with that of the
  magnet.
• At maximum torque, the magnetic field of the loop
  of current carrying wire is at 90o.
• The net force on the loop is the vector sum of
  all of the forces acting on all of the sides.
• When a loop with current is placed in a magnetic
  field, the loop will rotate such that its normal
  becomes aligned with the externally applied
  magnetic field.

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Torque on a Current Carrying Coil (cont.)

• What is the contribution of forces from the two
  shorter sides (w)?
• F IwB sin (90o ?)
• Note 1 ? is the angle that the normal to the
  wire makes with the direction of the magnetic
  field.
• Note 2 Due to symmetry, the forces on the two
  shorter sides will cancel each other out (Use RHR
  1).

X X X X X X X X
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Torque on a Current Carrying Coil (cont.)

• What is the contribution of torque from the two
  longer sides (L)?
• F BIL for each side since L is always
  perpendicular to B.
• The magnitude of the torque due to these forces
  is
• ? BIL (½w sin?) BIL (½w sin?) BILw sin? (1)
• Note Since Lw the area of the loop (A), (1)
  reduces to
• ? IAB sin?
• For a winding with N turns, this formula can be
  rewritten
• ? NIAB sin?

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DC Motor
DC Electric Motor
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Key Ideas

• Lorentz Force A charge moving perpendicular to a
  magnetic field will experience a force.
• Charged particles moving perpendicular to a
  magnetic field will travel in a circular orbit.
• The magnetic force does not change the kinetic
  energy of a moving charged particle only
  direction.
• The magnetic field (B) is a vector quantity with
  the unit of Tesla
• Use right hand rules to determine the
  relationship between the magnetic field, the
  velocity of a positively charged particle and the
  resulting force it experiences.