184_notes:i_b_force

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184_notes:i_b_force [2018/07/19 13:20] – [Force on a little chunk] curdemma184_notes:i_b_force [2018/07/19 13:30] – [Force on the whole wire] curdemma
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 Here we want to pick the limits of the integral to be from the starting point of the wire ($l_i$) to the end of the wire ($l_f$) so we are adding up over the whole length of the wire. This form of the force will //always// work to find the magnetic force on the whole wire - we have not made very many assumptions so far in coming up with this equation.  Here we want to pick the limits of the integral to be from the starting point of the wire ($l_i$) to the end of the wire ($l_f$) so we are adding up over the whole length of the wire. This form of the force will //always// work to find the magnetic force on the whole wire - we have not made very many assumptions so far in coming up with this equation. 
  
-However, if we do make a few assumptions we can simplify this equation significantly. We will start by //__assuming that the current in the wire is constant and in a steady state__//. This allows us to pull the current out of the integral, leaving:+However, if we do make a few assumptions we can simplify this equation significantly. We will start by //__assuming that the current in the wire is constant and in a steady state__//. This allows us to pull the current out of the integral as a constant, leaving:
 $$\vec{F}_{wire}= I \int_{l_i}^{l_f} d\vec{l} \times \vec{B}$$ $$\vec{F}_{wire}= I \int_{l_i}^{l_f} d\vec{l} \times \vec{B}$$
  
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 $$|\vec{F}_{wire}|=IBLsin(\theta)$$ $$|\vec{F}_{wire}|=IBLsin(\theta)$$
  
-{{  184_notes:week11_8.png?250}}+[{{  184_notes:week11_8.png?250|Use the right hand rule to determine the direction of the magnetic force}}]
  
-where |$\vec{F}_{wire}$| is the magnitude of the force on the whole wire, I is the current through the wire, B is the //external// magnetic field, L is the length of the wire, and $\theta$ is the angle between the magnetic field and the length of the wire. //__Remember though that this equation is only good for straight wires with constant current that are in a constant magnetic field - because of all the assumptions that we made to get to this point.__//+where |$\vec{F}_{wire}$| is the magnitude of the force on the whole wire, $I$ is the current through the wire, $B$ is the //external// magnetic field, $L$ is the length of the wire, and $\theta$ is the angle between the magnetic field and the length of the wire. //__Remember though that this equation is only good for straight wires with constant current that are in a constant magnetic field - because of all the assumptions that we made to get to this point.__//
  
 To find the direction of the magnetic force, we will need to use the [[184_notes:rhr|right hand rule]]. Just like we did with the moving charge, you point your fingers in the direction of the moving charges (or rather in the direction of the current/$d\vec{l}$), then curl your fingers in the direction of the external magnetic field. Your thumb then points in the direction of the force. To find the direction of the magnetic force, we will need to use the [[184_notes:rhr|right hand rule]]. Just like we did with the moving charge, you point your fingers in the direction of the moving charges (or rather in the direction of the current/$d\vec{l}$), then curl your fingers in the direction of the external magnetic field. Your thumb then points in the direction of the force.
  • 184_notes/i_b_force.txt
  • Last modified: 2021/07/13 11:58
  • by schram45