General Physics PHY 1112

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General Physics (PHY 1112)
Lecture 14

• Electricity and Magnetism
• Magnetism
• Amperes law
• Applications of magnetic forces

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Lightning Review

• Last lecture
• Magnetism
• Galvanometer
• Torque on a current loop

Review Problem A rectangular loop is placed in
a uniform magnetic field with the plane of the
loop perpendicular to the direction of the field.
If a current is made to flow through the loop in
the sense shown by the arrows, the field exerts
on the loop 1. a net force. 2. a net
torque. 3. a net force and a net torque. 4.
neither a net force nor a net torque.
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19.7 Motion of Charged Particle in magnetic field
Bin

• Consider positively charge particle moving in a
  uniform magnetic field.
• Suppose the initial velocity of the particle is
  perpendicular to the direction of the field.
• Then a magnetic force will be exerted on the
  particle

r
Where is it directed?

• and make it follow a circular path.

Remember that
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The magnetic force produces a centripetal
acceleration.
The particle travels on a circular trajectory
with a radius
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Example 1 Proton moving in uniform magnetic
field

• A proton is moving in a circular orbit of radius
  14 cm in a uniform magnetic field of magnitude
  0.35 T, directed perpendicular to the velocity of
  the proton. Find the orbital speed of the proton.

Given r 0.14 m B 0.35 T m 1.67x10-27
kg q 1.6 x 10-19 C
Recall that the protons radius would be
Thus
Find v ?
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Example 2
Consider the mass spectrometer. The electric
field between the plates of the velocity selector
is 950 V/m, and the magnetic fields in both the
velocity selector and the deflection chamber have
magnitudes of 0.930 T. Calculate the radius of
the path in the system for a singly charged ion
with mass m2.1810-26 kg.
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19.8 Magnetic Field of a long straight wire

• Danish scientist Hans Oersted (1777-1851)
  discovered (somewhat by accident) that an
  electric current in a wire deflects a nearby
  compass needle.
• In 1820, he performed a simple experiment with
  many compasses that clearly showed the presence
  of a magnetic field around a wire carrying a
  current.

I
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Magnetic Field due to Currents

• The passage of a steady current in a wire
  produces a magnetic field around the wire.
• Field form concentric lines around the wire
• Direction of the field given by the right hand
  rule.
• If the wire is grasped in the right hand with the
  thumb in the direction of the current, the
  fingers will curl in the direction of the field
  (second right-hand rule).
• Magnitude of the field

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Magnitude of the field
I
r
B
mo called the permeability of free space
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Amperes Law
Consider a circular path surrounding a current,
divided in segments Dl, Ampere showed that the
sum of the products of the field by the length of
the segment is equal to mo times the current.
Andre-Marie Ampere
I
r
B
Dl
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Consider a case where B is constant and uniform
Then one finds
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19.9 Magnetic Force between two parallel
conductors
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Force per unit length
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Definition of the SI unit Ampere
Used to define the SI unit of current called
Ampere.

• If two long, parallel wires 1 m apart carry the
  same current, and the magnetic force per unit
  length on each wire is 2x10-7 N/m, then the
  current is defined to be 1 A.

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Example 1 Levitating a wire

• Two wires, each having a weight per units length
  of 1.0x10-4 N/m, are strung parallel to one
  another above the surface of the Earth, one
  directly above the other. The wires are aligned
  north-south. When their distance of separation is
  0.10 mm what must be the current in each in order
  for the lower wire to levitate the upper wire.
  (Assume the two wires carry the same current).

l
1
I1
2
d
I2
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Two wires, each having a weight per units length
of 1.0x10-4 N/m, are strung parallel to one
another above the surface of the Earth, one
directly above the other. The wires are aligned
north-south. When their distance of separation is
0.10 mm what must be the current in each in order
for the lower wire to levitate the upper wire.
(Assume the two wires carry the same current).
F1
1
I1
B2
mg/l
2
d
I2
l
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Example 2 magnetic field between the wires
The two wires in the figure below carry currents
of 3.00A and 5.00A in the direction indicated.
Find the direction and magnitude of the magnetic
field at a point midway between the wires.
5.00 A
3.00 A
20.0 cm
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19.10 Magnetic Field of a current loop

• Magnetic field produced by a wire can be enhanced
  by having the wire in a loop.

Dx1
I
B
Dx2
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19.11 Magnetic Field of a solenoid

• Solenoid magnet consists of a wire coil with
  multiple loops.
• It is often called an electromagnet.

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Solenoid Magnet

• Field lines inside a solenoid magnet are
  parallel, uniformly spaced and close together.
• The field inside is uniform and strong.
• The field outside is non uniform and much weaker.
• One end of the solenoid acts as a north pole, the
  other as a south pole.
• For a long and tightly looped solenoid, the field
  inside has a value

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Solenoid Magnet

• n N/l number of (loop) turns per unit
  length.
• I current in the solenoid.

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Example Magnetic Field inside a Solenoid.

• Consider a solenoid consisting of 100 turns of
  wire and length of 10.0 cm. Find the magnetic
  field inside when it carries a current of 0.500 A.

N 100 l 0.100 m I 0.500 A
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ComparisonElectric Field vs. Magnetic Field
Electric Magnetic Source Charges Moving
Charges Acts on Charges Moving
Charges Force F Eq F q v B
sin(q) Direction Parallel
E Perpendicular to v,B
Field Lines Opposites Charges Attract
Currents Repel