184_notes:q_b_force

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184_notes:q_b_force [2018/07/03 13:53] – [Magnetic Force Equation] curdemma184_notes:q_b_force [2021/06/08 18:43] (current) – bartonmo
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 Section 20.1 in Matter and Interactions (4th edition) 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: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]]+[[184_notes:motiv_b_force|Previous Page: Magnetic Forces in the Real World]]*/
  
 ===== Magnetic Force on Moving Charges ===== ===== Magnetic Force on Moving Charges =====
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 {{youtube>oXL3FJO00UM?large}} {{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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 In terms of calculating the magnetic force, there are a couple of ways that we can go about the math. If you know the vector components of the velocity and magnetic field, one method you can use is the general [[183_notes:cross_product|cross product]] equation to calculate the force. This method will always work and will give you each of the components of the force, but it can be cumbersome to actually write out each component sometimes. In the other method, we can simplify the cross product to give us a magnitude of the force and we can use the [[184_notes:rhr|Right Hand Rule]] to figure out the direction. In terms of calculating the magnetic force, there are a couple of ways that we can go about the math. If you know the vector components of the velocity and magnetic field, one method you can use is the general [[183_notes:cross_product|cross product]] equation to calculate the force. This method will always work and will give you each of the components of the force, but it can be cumbersome to actually write out each component sometimes. In the other method, we can simplify the cross product to give us a magnitude of the force and we can use the [[184_notes:rhr|Right Hand Rule]] to figure out the direction.
  
-=== Magnitude of the Magnetic Force ===+===== Magnitude of the Magnetic Force =====
 We can find the magnitude of any general cross product using $|\vec{a} \times \vec{b} |= |\vec{a}| |\vec{b}| sin(\theta)$ where $\theta$ is the angle between $\vec{a}$ and $\vec{b}$. In terms of the magnetic force then, we can find the magnitude by using: We can find the magnitude of any general cross product using $|\vec{a} \times \vec{b} |= |\vec{a}| |\vec{b}| sin(\theta)$ where $\theta$ is the angle between $\vec{a}$ and $\vec{b}$. In terms of the magnetic force then, we can find the magnitude by using:
 $$F = q v B sin(\theta)$$ $$F = q v B sin(\theta)$$
 where F is the magnitude of the force, $q$ is the charge, $v$ is magnitude of the velocity (speed), and $B$ is the magnitude of the magnitude field. $\theta$ then is angle between the velocity of the charge and the magnetic field. This equation is often much easier to use and think about, but //it does not tell us anything about the direction of the force// - **only the magnitude**.  where F is the magnitude of the force, $q$ is the charge, $v$ is magnitude of the velocity (speed), and $B$ is the magnitude of the magnitude field. $\theta$ then is angle between the velocity of the charge and the magnetic field. This equation is often much easier to use and think about, but //it does not tell us anything about the direction of the force// - **only the magnitude**. 
  
-=== Direction of the Magnetic Force ===+===== Direction of the Magnetic Force =====
 Just like we did with the [[184_notes:moving_q|Biot-Savart Law]] in this weeks notes, 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]] in this weeks notes, 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. 
 [{{184_notes:Week11_1.png?200|RHR used to find resulting magnetic force on a moving positive charge  }}] [{{184_notes:Week11_1.png?200|RHR used to find resulting magnetic force on a moving positive charge  }}]
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