184_notes:linecharge

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
Next revisionBoth sides next revision
184_notes:linecharge [2021/02/13 19:13] – [Putting it together] bartonmo184_notes:linecharge [2021/05/25 14:30] schram45
Line 46: Line 46:
 $$\vec{E}=\int\frac{1}{4\pi\epsilon_0}\frac{Q}{L}\frac{dx}{(\frac{L}{2}+d-x)^2}\hat{x}$$ $$\vec{E}=\int\frac{1}{4\pi\epsilon_0}\frac{Q}{L}\frac{dx}{(\frac{L}{2}+d-x)^2}\hat{x}$$
  
-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:**
 $$\vec{E}=\int_{-\frac{L}{2}}^{\frac{L}{2}}\frac{1}{4\pi\epsilon_0}\frac{Q}{L}\frac{dx}{(\frac{L}{2}+d-x)^2}\hat{x}$$ $$\vec{E}=\int_{-\frac{L}{2}}^{\frac{L}{2}}\frac{1}{4\pi\epsilon_0}\frac{Q}{L}\frac{dx}{(\frac{L}{2}+d-x)^2}\hat{x}$$
  
Line 52: Line 52:
  
 ==== Examples ==== ==== Examples ====
-[[:184_notes:examples:Week4_charge_ring|Electric Field from a Ring of Charge]]+Video Example: 
 +{{youtube>I6cqhqIdG7A?large}} 
 +Written out work: [[:184_notes:examples:Week4_charge_ring|Electric Field from a Ring of Charge]]
  
 /*[[: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.txt
  • Last modified: 2021/07/22 18:17
  • by schram45