184_notes:moving_q

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184_notes:moving_q [2017/10/24 01:11] – dmcpadden184_notes:moving_q [2018/05/15 16:04] – curdemma
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 Section 17.3 in Matter and Interactions (4th edition) Section 17.3 in Matter and Interactions (4th edition)
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 +[[184_notes:rhr|Next Page: Right Hand Rule]]
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 +[[184_notes:mag_interaction|Previous Page: Magnetic Interaction]]
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 ===== Moving Charges Make Magnetic Fields ===== ===== Moving Charges Make Magnetic Fields =====
 Just like we did with electric fields, we will start with magnetic fields by looking at the simplest source: a single moving point charge. When we are talking about this moving charge and the corresponding magnetic field, there are intuitive qualities that we want to make sure our mathematical model includes: (1) the farther away the observation point is from the moving charge, the smaller that we expect the magnetic field to be; (2) the larger the amount of charge, the larger we expect the magnetic field to be; and (3) the faster the charge is moving, the larger we expect the magnetic field to be. The final piece that is perhaps not so intuitive is that the direction of the magnetic field is actually perpendicular to observation point and to the velocity vector. However, each of these demands is consistent with experimental observations of moving charges. These notes will detail the mathematical equation that we use for the magnetic field (only for a single moving point charge) and explain a new tool called the [[184_notes:rhr|Right Hand Rule]] that we can use to find the direction.      Just like we did with electric fields, we will start with magnetic fields by looking at the simplest source: a single moving point charge. When we are talking about this moving charge and the corresponding magnetic field, there are intuitive qualities that we want to make sure our mathematical model includes: (1) the farther away the observation point is from the moving charge, the smaller that we expect the magnetic field to be; (2) the larger the amount of charge, the larger we expect the magnetic field to be; and (3) the faster the charge is moving, the larger we expect the magnetic field to be. The final piece that is perhaps not so intuitive is that the direction of the magnetic field is actually perpendicular to observation point and to the velocity vector. However, each of these demands is consistent with experimental observations of moving charges. These notes will detail the mathematical equation that we use for the magnetic field (only for a single moving point charge) and explain a new tool called the [[184_notes:rhr|Right Hand Rule]] that we can use to find the direction.     
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 We could also get this result using the [[184_notes:rhr|Right Hand Rule]], which says that if you point your fingers in the direction of the first vector (the velocity vector in this case) and curl the towards the direction of the second vector (the separation vector in this case), your thumb will point in the direction of the cross product (or the B-field direction here). If you do this - point your right hand fingers in the direction of +x and curl them toward +y direction, your thumb will point in the +z direction or out of the page. **NOTE: the right hand rule is true for POSITIVE charges**. If you have a negative charge, you can //either// use your left hand or just flip the direction of your final vector (i.e. if you get +z for your right hand rule, you would have a direction of -z for a negative charge).   We could also get this result using the [[184_notes:rhr|Right Hand Rule]], which says that if you point your fingers in the direction of the first vector (the velocity vector in this case) and curl the towards the direction of the second vector (the separation vector in this case), your thumb will point in the direction of the cross product (or the B-field direction here). If you do this - point your right hand fingers in the direction of +x and curl them toward +y direction, your thumb will point in the +z direction or out of the page. **NOTE: the right hand rule is true for POSITIVE charges**. If you have a negative charge, you can //either// use your left hand or just flip the direction of your final vector (i.e. if you get +z for your right hand rule, you would have a direction of -z for a negative charge).  
-==== Superposition ==== 
-{{  184_notes:Week9_3.png?200}} 
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-Superposition is central to understanding of all E&M fields and governs how all of these fields add up. That is, magnetic field vectors superpose just as you might expect. This means that if you have two moving charges, the magnetic field at any given point is given by the vector addition of the magnetic field due to one of the moving charges //plus// the magnetic field due to the other moving charge. 
-$$\vec{B}_{total}=\vec{B}_1+\vec{B}_2$$ 
-This idea scales for as many moving charges as you have: 
-$$\vec{B}_{total}=\vec{B}_1+\vec{B}_2+\vec{B}_3+\vec{B}_4+...$$ 
-However, if you have both electric and magnetic fields you **cannot** just add together the magnetic and electric fields. These are different quantities with different units; therefore, they do not add together (this would be like trying to add time to mass - it's just not a thing you can do).  
  
-{{youtube>dZxoWgE1Hb4?large}} 
 ==== Examples ==== ==== Examples ====
 [[:184_notes:examples:Week9_detecting_b|Magnetic Field near a Moving Charge]] [[:184_notes:examples:Week9_detecting_b|Magnetic Field near a Moving Charge]]
  • 184_notes/moving_q.txt
  • Last modified: 2021/07/05 21:51
  • by schram45