184_notes:q_b_force

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184_notes:q_b_force [2017/10/24 15:06] – dmcpadden184_notes:q_b_force [2018/05/15 16:22] – curdemma
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 +Section 20.1 in Matter and Interactions (4th edition)
 +
 +[[184_notes:q_path|Next Page: Path of a Moving Charge through a Magnetic Field]]
 +
 +[[184_notes:motiv_b_force|Previous Page: Magnetic Forces in the Real World]]
 +
 ===== Magnetic Force on Moving Charges ===== ===== Magnetic Force on Moving Charges =====
 We'll start thinking about the magnetic force in terms of the simplest case: a single moving charge through an external magnetic field. The source of the external magnetic field could be another moving charge, a current, a bar magnet or any combination of those. Most of the time though, we will concern ourselves with how the charge interacts with the field (whatever it may be) and we will not care as much about what produces that magnetic field. These notes will describe how we can calculate the force from the magnetic field, including the magnitude and direction of that force.   We'll start thinking about the magnetic force in terms of the simplest case: a single moving charge through an external magnetic field. The source of the external magnetic field could be another moving charge, a current, a bar magnet or any combination of those. Most of the time though, we will concern ourselves with how the charge interacts with the field (whatever it may be) and we will not care as much about what produces that magnetic field. These notes will describe how we can calculate the force from the magnetic field, including the magnitude and direction of that force.  
  
 +{{youtube>oXL3FJO00UM?large}}
 ==== Magnetic Force Equation ==== ==== Magnetic Force Equation ====
 Mathematically, the magnetic force on a moving charge from an //external// magnetic field is given by: Mathematically, the magnetic force on a moving charge from an //external// magnetic field is given by:
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 === Direction of the Magnetic Force === === Direction of the Magnetic Force ===
 +{{184_notes:Week11_1.png?200  }}
 Just like we did with the [[184_notes:moving_q|Biot-Savart Law]], we can use the [[184_notes:rhr|right hand rule]] to think about the direction of the magnetic force. To use the right hand rule, remember that you point the fingers on your right hand in the direction of the first vector in the cross product and curl them toward the direction of the second vector. Then if you stick out your thumb that will be the direction of the cross product. For the magnetic force then, you point your fingers in the direction of the velocity, then curl them toward the direction of the magnetic field, and your thumb will point in the direction of the force.  Just like we did with the [[184_notes:moving_q|Biot-Savart Law]], we can use the [[184_notes:rhr|right hand rule]] to think about the direction of the magnetic force. To use the right hand rule, remember that you point the fingers on your right hand in the direction of the first vector in the cross product and curl them toward the direction of the second vector. Then if you stick out your thumb that will be the direction of the cross product. For the magnetic force then, you point your fingers in the direction of the velocity, then curl them toward the direction of the magnetic field, and your thumb will point in the direction of the force. 
  
-FIXME Add Picture 11.1/11.2+{{  184_notes:week11_2.png?200}}
  
 For example, if the charge is moving to the right ($+\hat{x}$ direction) through a magnetic field that points into the page ($-\hat{z}$ direction), you should find that the force on the charge points up ($+\hat{y}$ direction).  Note that **the right hand rule works for positive charges** - if the charge is negative, you have to either remember to flip the direction of the force at the end (i.e. the force would point in the $-\hat{y}$ direction if the charge was negative) or use your //left hand// (but the same process - fingers still point in the direction of the velocity and curl toward the B-field). For example, if the charge is moving to the right ($+\hat{x}$ direction) through a magnetic field that points into the page ($-\hat{z}$ direction), you should find that the force on the charge points up ($+\hat{y}$ direction).  Note that **the right hand rule works for positive charges** - if the charge is negative, you have to either remember to flip the direction of the force at the end (i.e. the force would point in the $-\hat{y}$ direction if the charge was negative) or use your //left hand// (but the same process - fingers still point in the direction of the velocity and curl toward the B-field).
  
 +==== Examples ====
 +[[:184_notes:examples:Week10_force_on_charge|Magnetic Force on a Moving Charge]]
  • 184_notes/q_b_force.txt
  • Last modified: 2021/06/08 18:43
  • by bartonmo