184_notes:linecharge

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184_notes:linecharge [2021/02/13 19:13] – [Putting it together] bartonmo184_notes:linecharge [2021/07/22 18:17] (current) – schram45
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 $$\vec{E}=\int\frac{1}{4\pi\epsilon_0}\frac{Q}{L}\frac{dx}{(\frac{L}{2}+d-x)^2}\hat{x}$$ $$\vec{E}=\int\frac{1}{4\pi\epsilon_0}\frac{Q}{L}\frac{dx}{(\frac{L}{2}+d-x)^2}\hat{x}$$
  
-The final piece that we need to add is limits to the integral. Since the piece of tape stretches from $-\frac{L}{2}$ to $\frac{L}{2}$, this means that the limits on the integral should also go from $-\frac{L}{2}$ to $\frac{L}{2}$ - conceptually this means that we want to add up the little bits of charge __only__ along the length of the line. This gives us a final integral of:+The final piece that we need to add is limits to the integral. Since the piece of tape stretches from $-\frac{L}{2}$ to $\frac{L}{2}$, this means that the limits on the integral should also go from $-\frac{L}{2}$ to $\frac{L}{2}$ - conceptually this means that we want to add up the little bits of charge //only// along the length of the line. **This gives us a final integral of:**
 $$\vec{E}=\int_{-\frac{L}{2}}^{\frac{L}{2}}\frac{1}{4\pi\epsilon_0}\frac{Q}{L}\frac{dx}{(\frac{L}{2}+d-x)^2}\hat{x}$$ $$\vec{E}=\int_{-\frac{L}{2}}^{\frac{L}{2}}\frac{1}{4\pi\epsilon_0}\frac{Q}{L}\frac{dx}{(\frac{L}{2}+d-x)^2}\hat{x}$$
  
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 ==== Examples ==== ==== Examples ====
-[[:184_notes:examples:Week4_charge_ring|Electric Field from a Ring of Charge]]+  * [[:184_notes:examples:Week4_charge_ring|Electric Field from a Ring of Charge]] 
 +    * Video Example: Electric Field from a Ring of Charge 
 +  * [[:184_notes:examples:Week4_charge_cylinder|Super Challenge Problem: Electric field from a Cylinder of Charge]] 
 +    * Video Example: Electric Field from a Cylinder of Charge 
 +{{youtube>I6cqhqIdG7A?large}} 
 +{{youtube>LeIp7rrwchw?large}}
  
 /*[[:184_notes:examples:Week4_charge_cylinder|Super Challenge Problem: Electric field from a Cylinder of Charge]]*/ /*[[:184_notes:examples:Week4_charge_cylinder|Super Challenge Problem: Electric field from a Cylinder of Charge]]*/
  • 184_notes/linecharge.1613243587.txt.gz
  • Last modified: 2021/02/13 19:13
  • by bartonmo