The final piece that we need to add is limits to the integral. Since the piece of tape stretches from −L2 to L2, this means that the limits on the integral should also go from −L2 to L2 - 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 −L2 to L2, this means that the limits on the integral should also go from −L2 to L2 - 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:**
→E=∫L2−L214πϵ0QLdx(L2+d−x)2ˆx
→E=∫L2−L214πϵ0QLdx(L2+d−x)2ˆx
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Line 52:
==== Examples ====
==== Examples ====
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[[:184_notes:examples:Week4_charge_ring|Electric Field from a Ring of Charge]]
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* [[:184_notes:examples:Week4_charge_ring|Electric Field from a Ring of Charge]]
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* Video Example: Electric Field from a Ring of Charge
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* [[:184_notes:examples:Week4_charge_cylinder|Super Challenge Problem: Electric field from a Cylinder of Charge]]
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* Video Example: Electric Field from a Cylinder of Charge
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{{youtube>I6cqhqIdG7A?large}}
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{{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]]*/