Phy2049: Magnetism

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Phy2049 Magnetism

• Last lecture Biot-Savarts and Amperes law
• Magnetic Field due to a straight wire
• Current loops (whole or bits)and solenoids
• Today reminder and Faradays law.

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hitt

• Two long straight wires pierce the plane of the
  paper at vertices of an equilateral triangle as
  shown. They each carry 3A but in the opposite
  direction. The wire on the left has the current
  coming out of the paper while the wire on the
  right carries the current going into the paper.
  The magnetic field at the third vertex (P) has
  the magnitude and direction
• (North is up)
• (1) 20 µT, east (2) 17 µT, west (3) 15 µT, north
  (4) 26 µT, south (5) none of these

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Magnetic Field Units

• From the expression for force on a
  current-carrying wire
• B Fmax / I L
• Units Newtons/A?m ? Tesla (SI unit)
• Another unit 1 gauss 10-4 Tesla
• Some sample magnetic field strengths
• Earth B 0.5 gauss 0.5 x 10-4 T
• Galaxy B ? 10-6 gauss 10-10 T
• Bar magnet B ? 100 200 gauss
• Strong electromagnet B 2 T
• Superconducting magnet B 5 10 T
• Pulse magnet B ? 100 T
• Neutron star B ? 108 109 T
• Magnetar B ? 1011 T

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Force Between Two Parallel Currents

• Force on I2 from I1
• RHR ? Force towards I1
• Force on I1 from I2
• RHR ? Force towards I2
• Magnetic forces attract two parallel currents

I1
I2
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Force Between Two Anti-Parallel Currents

• Force on I2 from I1
• RHR ? Force away from I1
• Force on I1 from I2
• RHR ? Force away from I2
• Magnetic forces repel two antiparallel currents

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Parallel Currents (cont.)

• Look at them edge on to see B fields more clearly

B
B
Antiparallel repel
2
1
2
1
F
F
B
B
2
1
Parallel attract
1
2
F
F
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B Field _at_ Center of Circular Current Loop

• Radius R and current i find B field at center of
  loop
• Direction RHR 3 (see picture)
• If N turns close together

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Current Loop Example

• i 500 A, r 5 cm, N20

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B Field of Solenoid

• Formula found from Amperes law
• i current
• n turns / meter
• B constant inside solenoid
• B zero outside solenoid
• Most accurate when LgtgtR
• Example i 100A, n 10 turns/cm
• n 1000 turns / m

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Field at Center of Partial Loop

• Suppose loop covers angle ?
• Use example where ? ? (half circle)
• Define direction into page as positive

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Partial Loops (cont.)

• Note on problems when you have to evaluate a B
  field at a point from several partial loops
• Only loop parts contribute, proportional to angle
  (previous slide)
• Straight sections aimed at point contribute
  exactly nothing
• Be careful about signs, e.g.in (b) fields
  partially cancel, whereas in (a) and (c) they add

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Chapter 30 Induction and Inductance In
this chapter we will study the following topics
-Faradays law of
induction
-Lenzs rule

-Electric field
induced by a changing magnetic field
-Inductance and mutual
inductance
- RL circuits

-Energy stored in a
magnetic field
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hitt

• A horizontal power line carries a current of 5000
  A from south to north. Earth's magnetic eld (60
  µT) is directed towards north and inclined
  down-ward 50 degrees to the horizontal. Find the
  magnitude and direction of the magnetic force on
  100 m of the line due to the Earth's field.
• 23 N, west (2) 23 N, east (3) 30N, west
• (4) 30N, east (5) none of these