Chapter 29. Magnetic Field Due to Currents

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Chapter 29. Magnetic Field Due to Currents

• 29.1. What is Physics?      
• 29.2. Calculating the Magnetic Field Due to a
  Current      
• 29.3. Force Between Two Parallel Currents      
• 29.4. Ampere's Law      
• 29.5. Solenoids and Toroids      
• 29.6. A Current-Carrying Coil as a Magnetic Dipole

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What is Physics?
    
                                                                                                                         

A moving charged particle produces a magnetic
field around itself
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Magnetic Field Due to a Current
                                                                                             

The permeability constant, whose value is defined
to be exactly
A length vector     that has length ds and
whose direction is the direction of the current
in ds.

                                                                                                                                                  
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Magnetic Field Due to a Current in a Long
Straight Wire
                                                                 

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Magnetic field lines produced by a current in a
long straight wire
                                                                                                                                                                                    

                                                                                                              

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Right-hand rule
                                                                    

• Grasp the element in your right hand with your
  extended thumb pointing in the direction of the
  current. Your fingers will then naturally curl
  around in the direction of the magnetic field
  lines due to that element.

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Magnetic Field Due to a Current in a Circular Arc
of Wire
                                                               

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A Current-Carrying Coil as a Magnetic Dipole

                                                                  
For a loop, ?2p, at the center of the loop
If
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Sample Problem
The wire in Fig. 29-8a carries a current i and
consists of a circular arc of radius R and
central angle      rad, and two straight
sections whose extensions intersect the center C
of the arc. What magnetic field     does the
current produce at C?
                                                                                                                                                                     

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Example  Finding the Net Magnetic Field

• A long, straight wire carries a current of
  I18.0 A. As Figure 21.31a illustrates, a
  circular loop of wire lies immediately to the
  right of the straight wire. The loop has a radius
  of R0.030 m and carries a current of I22.0 A.
  Assuming that the thickness of the wires is
  negligible, find the magnitude and direction of
  the net magnetic field at the center C of the
  loop.

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Two Current-Carrying Wires Exert Magnetic Forces
on One Another

• To find the force on a current-carrying wire due
  to a second current-carrying wire, first find the
  field due to the second wire at the site of the
  first wire. Then find the force on the first wire
  due to that field.
• Parallel currents attract each other, and
  antiparallel currents repel each other.

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 Ampere's Law
                                                                                          

                                                                                                             

• The loop on the integral sign means that is to be
  integrated around a closed loop, called an
  Amperian loop. The current ienc is the net
  current encircled by that closed loop.
• Curl your right hand around the Amperian loop,
  with the fingers pointing in the direction of
  integration. A current through the loop in the
  general direction of your outstretched thumb is
  assigned a plus sign, and a current generally in
  the opposite direction is assigned a minus sign.

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Example An Infinitely Long, Straight,
Current-Carrying Wire

• Use Amperes law to obtain the magnetic field
  produced by the current in an infinitely long,
  straight wire.

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Magnetic Field Inside a Long Straight Wire with
uniformly distributed Current
                                                                                                     

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A LOOP OF Current

• For a single loop, the magnetic field at the
  center is Bµ0I/(2R)
• For a loop with N turns of wire,

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Comparison a loop wire and a bar magnet

• loop wire

                                                                                                              

• bar magnet

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Magnetic Field of a Solenoid
                 

                                                                                                                                                                           

                                                                                                              

                                                                        

                                                                                                              

For a long ideal solenoid
where n is the number of turns per unit length of
the solenoid
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Magnetic Field of a Toroid
                                                                                                 

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Example  

• A solenoid is 0.50 m long, has three layers of
  windings of 750 turns each, and carries a current
  of 4.0 A. What is the magnetic field at the
  center of the solenoid?

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Example  
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Example  
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Example  
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Example