Lecture 9 Magnetic Fields due to Currents Chp. 30

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Lecture 9 Magnetic Fields due to Currents Chp. 30

• Cartoon - Shows magnetic field around a long
  current carrying wire and a loop of wire
• Opening Demo - Iron filings showing B fields
  around wires with currents
• Warm-up problem
• Physlet
• Topics
• Magnetic field produced by a moving charge
• Magnetic fields produced by currents. BigBite as
  an example.
• Using Biot Savart Law to calculate magnetic
  fields produced by currents.
• Examples Field at center of loop of wire, at
  center of circular arc of wire, at center of
  segment of wire.
• Amperes Law Analogous to Gauss Law in
  electrostatics, Useful in symmetric cases.
• Infinitely long straight wire of radius a. Find B
  outside and inside wire.
• Solenoid and Toroid Find B field.
• Forces between current carrying wires or parallel
  moving charges
• Demos
• Torque on a current loop(galvanometer)
• Iron filings showing B fields around wires with
  currents.
• Compass needle near current carrying wire
• BigBite as an example of using a magnet as a
  research tool.

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Magnetic Fields due to Currents

• Torque on a coil in a magnetic field demo left
  over from last time
• So far we have used permanent magnets as our
  source of magnetic field. Historically this is
  how it started.
• In early decades of the last century, it was
  learned that moving charges and electric currents
  produced magnetic fields.
• How do you find the Magnetic field due to a
  moving point charge?
• How do you find the Magnetic field due to a
  current?
• Biot-Savart Law direct integration
• Amperes Law uses symmetry
• Examples and Demos

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Crossed magnetic and electric fields
y
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Discovery of the electron by J.J. Thompson in 1897

1. E0, B0 Observe spot on screen

2. Set E to some value and measure y the
deflection
3. Now turn on B until spot returns to the
oriiginal position
This ratio was first measured by Thompson to be
lighter than hydrogen by 1000
4 Solve for
Show demo of CRT
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Hall Effect Crossed fields to measure charge
carrier density n
VEd
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Topic

• A moving charge produces a magnetic field.

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Example

• A point charge q 1 mC moves in the x
  direction with v 108 m/s. It misses a mosquito
  by 1 mm. What is the B field experienced by the
  mosquito?

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To find the E field of a charge distribution use
Use
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Topic Biot Savart Law
Loop of wire lying in a plane. It has radius R
and total current i flowing in it.
Magnitude of B field at center of loop. Direction
is out of paper.
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Example

• Loop of wire of radius R 5 cm and current
  i 10 A. What is B at the center? Magnitude and
  direction

Direction is out of the page.
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What is the B field at the center of a segment or
circular arc of wire?
P
Why is the contribution to the B field at P equal
to zero from the straight section of wire?
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Find magnetic field at center of arc length
Suppose you had the following loop.
What is the magnitude and direction of B at the
origin?
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Next topic Amperes Law
Allows us to solve certain highly symmetric
current problems for the magnetic field as Gauss
Law did in electrostatics.
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Example Use Amperes Law to find B near a very
long, straight wire. B is independent of position
along the wire and only depends on the distance
from the wire (symmetry).
Show Fe fillings around a straight wire with
current, current loop, and solenoid.
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Rules for finding direction of B field from a
current flowing in a wire
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Force between two current carrying wires
Find the force due to the current element of the
first wire and the magnetic field of the second
wire. Integrate over the length of both wires.
This will give the force between the two wires.
and directed towards wire a (wires are
attracted).
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Example Find magnetic field inside a long, thick
wire of radius a
IC current enclosed by the path
Example Find field inside a solenoid. See next
slide.
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Solenoid
n is the number of turns per meter
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First evaluate the right side, its easy
IC nhi
Right side ?0nhi
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Evaluate left side
Bh 0 0 0
Bh ?0nhi
B ?0ni
n the number of loops or turns per meter
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Toroid
N is the total number of turns
Tokamak Toroid at Princeton I 73,000 Amps for 3
secs B 5.2 T
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Magnetic dipole inverse cube law
z
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Warm up Problem Set 9

• Warm up set 9 Due 800 am Thursday
• HRW6 30.TB.02. 119973 A "coulomb" is
• one ampere per second
• an abbreviation for a certain combination of
  kilogram, meter and second
• the quantity of charge which will exert a
  force of 1 N on a similar charge at a distance of
  1 m
• the amount of current in each of two long
  parallel wires separated by 1 m,
• which produces a force of 2 10-7 N per meter
• the amount of charge which flows past a point
  in one second when the current is 1 A
• 2. HRW6 30.TB.03. 119974 Electrons are going
  around a circle in a counterclockwise direction
  as shown.
• At the center of the circle they produce a
  magnetic field that is
• to the left
• into the page
• out of the page
• zero
• to the right