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184_notes:b_summary [2018/03/19 17:43] – [Models of magnetic field] curdemma184_notes:b_summary [2021/06/16 22:14] (current) – bartonmo
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 +/*[[184_notes:i_b_force|Previous Page: Magnetic Force on Current Carrying Wires]]
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 +[[184_notes:e_b_summary|Next Page: Summary of Electricity and Magnetism (thus far)]]*/
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 ===== Summary of Magnetic Fields and Force ===== ===== Summary of Magnetic Fields and Force =====
      
 It is an experimental fact that moving electric charges generate magnetic fields in all of space. When we observe a magnetic field, we know that is often due to some charge or collection of charges that are moving relative to our location in space (unless it’s due to a changing electric field as we will see soon).  It is an experimental fact that moving electric charges generate magnetic fields in all of space. When we observe a magnetic field, we know that is often due to some charge or collection of charges that are moving relative to our location in space (unless it’s due to a changing electric field as we will see soon). 
  
-==== Models of magnetic field ====+===== Models of Magnetic Field =====
  
 The [[184_notes:moving_q|model of the magnetic field generate by a moving point charge]] is a bit more complicated than that for the electric field of a point charge because we observe that the magnetic field points perpendicular to the velocity vector and relation position vector, The [[184_notes:moving_q|model of the magnetic field generate by a moving point charge]] is a bit more complicated than that for the electric field of a point charge because we observe that the magnetic field points perpendicular to the velocity vector and relation position vector,
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 This is called the Biot-Savart Law, but is really just an expression for superposition of the magnetic field. Later we will find that the pattern of the magnetic field in some cases suggests a short cut to finding the magnetic field that doesn’t involve superposition integrals. This is called the Biot-Savart Law, but is really just an expression for superposition of the magnetic field. Later we will find that the pattern of the magnetic field in some cases suggests a short cut to finding the magnetic field that doesn’t involve superposition integrals.
  
-==== Magnetic force ====+===== Magnetic Force =====
  
 Magnetic fields can exert forces on moving charges, but these forces are always perpendicular to the motion of said charges. The [[184_notes:q_b_force|model for a single point charge in the presence of a magnetic field]] is: Magnetic fields can exert forces on moving charges, but these forces are always perpendicular to the motion of said charges. The [[184_notes:q_b_force|model for a single point charge in the presence of a magnetic field]] is:
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 →dF=Id→l×→B⟶→F=∫Id→l×→B
 →dF=Id→l×→B⟶→F=∫Id→l×→B
  
-Typically, the most common experience people have with magnetic force comes from permanent magnets, where the story is more complicated. We haven’t dived into the mathematical model for how forces in that situation work because while superposition continues to work, it means computing every magnetic field generated by every domain in one magnet and determining the force exerted on each domain of the other magnet and adding that all up!+Typically, the most common experience people have with magnetic force comes from permanent magnets, where the story is more complicated. We haven’t gotten into the mathematical model for how forces in that situation work because while superposition continues to work, it means computing every magnetic field generated by every domain in one magnet and determining the force exerted on each domain of the other magnet and adding that all up!
  
-==== Work and Energy ====+===== Work and Energy =====
  
-The definition of magnetic force shows us that [[184_notes:q_path#Work_Done|magnetic forces cannot change the kinetic energy]] of particles - the force is always perpendicular to the motion, so magnetic fields can not do work! Magnetic forces are used to [[184_notes:q_path|change the trajectory of moving charges]] without adding energy to them. This is very useful in applications like mass spectroscopy.+The definition of magnetic force shows us that [[184_notes:q_path#Work_Done|magnetic forces cannot change the kinetic energy]] of particles - //**the force is always perpendicular to the motion, so magnetic fields can not do work!**// Magnetic forces are used to [[184_notes:q_path|change the trajectory of moving charges]] without adding energy to them. This is very useful in applications like mass spectroscopy.
  
 However, this leads to a little bit of a difference between electric and magnetic fields, which is that there’s no such thing as a scalar magnetic potential (unlike [[184_notes:pc_potential|electric potential]]). This doesn’t mean there’s no such thing as magnetic energy - there most definitely is, but it is a more complex and abstract idea than we had for electric fields. In fact, because there are no magnetic monopoles, we can define a vector potential for magnetic field, which carries with it some information related to energy, but that is beyond the scope of this course. However, this leads to a little bit of a difference between electric and magnetic fields, which is that there’s no such thing as a scalar magnetic potential (unlike [[184_notes:pc_potential|electric potential]]). This doesn’t mean there’s no such thing as magnetic energy - there most definitely is, but it is a more complex and abstract idea than we had for electric fields. In fact, because there are no magnetic monopoles, we can define a vector potential for magnetic field, which carries with it some information related to energy, but that is beyond the scope of this course.
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