184_notes:moving_q

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184_notes:moving_q [2019/03/13 23:09] – dmcpadden184_notes:moving_q [2021/07/05 21:51] (current) – schram45
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 Section 17.3 in Matter and Interactions (4th edition) Section 17.3 in Matter and Interactions (4th edition)
  
-[[184_notes:rhr|Next Page: Right Hand Rule]]+/*[[184_notes:rhr|Next Page: Right Hand Rule]]
  
-[[184_notes:mag_interaction|Previous Page: Magnetic Interaction]]+[[184_notes:mag_interaction|Previous Page: Magnetic Interaction]]*/
  
 ===== Moving Charges Make Magnetic Fields ===== ===== Moving Charges Make Magnetic Fields =====
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 {{youtube>A4Nfu5r0eyU?large}} {{youtube>A4Nfu5r0eyU?large}}
-==== Mathematical Model for Magnetic Field ====+===== Mathematical Model for Magnetic Field =====
  
-We have already stated that the magnetic field is a //vector field//, meaning it has both magnitude and direction. As you will read soon, the magnetic field can also be related to the magnetic force. Again, we will start by making the //__point particle assumption - meaning that we will take our charged object and crush it down to single small point that has some mass and charge__//. Only this time, //__we will be considering the case where the point charge is moving with a **constant** velocity__//, rather than being fixed in one place.+We have already stated that the magnetic field is a vector field, meaning it has both //magnitude// and //direction//. As you will read soon, the magnetic field can also be related to the magnetic force. Again, we will start by making the //__point particle assumption - meaning that we will take our charged object and crush it down to single small point that has some mass and charge__//. Only this time, //__we will be considering the case where the point charge is moving with a **constant** velocity__//, rather than being fixed in one place.
  
-==== Magnetic Field Equation for a Moving Point Charge ====+===== Magnetic Field Equation for a Moving Point Charge =====
  
 The general equation for the magnetic field (→B), with units of Tesla (T), at some Point P due to a moving charge is given by: The general equation for the magnetic field (→B), with units of Tesla (T), at some Point P due to a moving charge is given by:
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 Together, these pieces tell you how the magnetic field from a point charge changes in space. The main take away here is: **the magnetic field is created by //moving// charges, points in a perpendicular direction, and can be calculated for every point in space around the charge**. The examples below show a few instances of how to calculate the magnetic field and how to use the Right Hand Rule to figure out the direction. Together, these pieces tell you how the magnetic field from a point charge changes in space. The main take away here is: **the magnetic field is created by //moving// charges, points in a perpendicular direction, and can be calculated for every point in space around the charge**. The examples below show a few instances of how to calculate the magnetic field and how to use the Right Hand Rule to figure out the direction.
  
-==== Magnetic Field Vectors ====+===== Magnetic Field Vectors =====
 Just like we did before with stationary charges, we will often draw the magnetic field vectors (or just B-field vectors) around the moving charge to help us understand what is happening to the magnetic field. **The magnitude of these vectors represents the magnitude of the magnetic field, and the direction of these vectors points in the direction of the magnetic field.**  Just like we did before with stationary charges, we will often draw the magnetic field vectors (or just B-field vectors) around the moving charge to help us understand what is happening to the magnetic field. **The magnitude of these vectors represents the magnitude of the magnetic field, and the direction of these vectors points in the direction of the magnetic field.** 
  
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 [{{  184_notes:Week9_2.png?200|Example set up}}] [{{  184_notes:Week9_2.png?200|Example set up}}]
  
-For example, consider a charge q moving in the +ˆx direction. We want to know the magnetic field at point P that is a distance d away from the charge in the ˆy direction at the instant the moving change is at the origin. Here, notice that must specific when we want to find the magnetic field as the change before or after that time will be at a different location -- it's moving, remember? We can find the magnetic field by using the equation above:+For example, consider a charge q moving in the +ˆx direction. We want to know the magnetic field at point P, which is a distance d away from the charge in the ˆy direction at the instant the moving change is at the origin (see the set up below). Here, notice that we must be specific about //when// we want to find the magnetic field. Because the charge is moving, it will be at a different location at different times -- //our solution is only accurate for a particular time/location of the charge//. We can find the magnetic field by using the equation above:
 →B=μ04πq→v×→rr3 →B=μ04πq→v×→rr3
 where our separation vector is →r=dˆy since it points from the charge to our point of interest. In this case then: where our separation vector is →r=dˆy since it points from the charge to our point of interest. In this case then:
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 ==== 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]] 
 +    * Video Example: Magnetic Field near a Moving Charge 
 +{{youtube>QgFjS7YcutQ?large}}
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