Electric Potential III Fields Potential Conductors Potential and
![Electric Potential (III) - Fields - Potential - Conductors Electric Potential (III) - Fields - Potential - Conductors](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-1.jpg)
![Potential and Continuous Charge Distributions We can use two completely different methods: 1. 2. Potential and Continuous Charge Distributions We can use two completely different methods: 1. 2.](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-2.jpg)
![Ex 1: Given V=3 x 2+12 x-1, find where E=0. Ex 1: Given V=3 x 2+12 x-1, find where E=0.](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-3.jpg)
![Ex 2: The Electric Potential of a Dipole y a -q a +q P Ex 2: The Electric Potential of a Dipole y a -q a +q P](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-4.jpg)
![Solution Solution](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-5.jpg)
![Ex 3: Find the potential of a finite line charge at P, AND the Ex 3: Find the potential of a finite line charge at P, AND the](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-6.jpg)
![Solution Solution](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-7.jpg)
![Ex 3: Find the potential of a uniformly charged sphere of radius R, inside Ex 3: Find the potential of a uniformly charged sphere of radius R, inside](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-8.jpg)
![Uniformly Charged Sphere, radius R E R r V Uniformly Charged Sphere, radius R E R r V](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-9.jpg)
![Recall that the electric field inside a solid conducting sphere with charge Q on Recall that the electric field inside a solid conducting sphere with charge Q on](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-10.jpg)
![Solution -Inside (r<R), E=0, integral of zero = constant, so V=const -Outside (r>R), E Solution -Inside (r<R), E=0, integral of zero = constant, so V=const -Outside (r>R), E](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-11.jpg)
![Solid Conducting Sphere, radius R E R r V Solid Conducting Sphere, radius R E R r V](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-12.jpg)
![Quiz A charge +Q is placed on a spherical conducting shell. What is the Quiz A charge +Q is placed on a spherical conducting shell. What is the](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-13.jpg)
![Calculating V from Sources: i) Point source: (note: V 0 as r ) or Calculating V from Sources: i) Point source: (note: V 0 as r ) or](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-14.jpg)
- Slides: 14
![Electric Potential III Fields Potential Conductors Electric Potential (III) - Fields - Potential - Conductors](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-1.jpg)
Electric Potential (III) - Fields - Potential - Conductors
![Potential and Continuous Charge Distributions We can use two completely different methods 1 2 Potential and Continuous Charge Distributions We can use two completely different methods: 1. 2.](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-2.jpg)
Potential and Continuous Charge Distributions We can use two completely different methods: 1. 2. Or, Find from Gauss’s Law, then…
![Ex 1 Given V3 x 212 x1 find where E0 Ex 1: Given V=3 x 2+12 x-1, find where E=0.](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-3.jpg)
Ex 1: Given V=3 x 2+12 x-1, find where E=0.
![Ex 2 The Electric Potential of a Dipole y a q a q P Ex 2: The Electric Potential of a Dipole y a -q a +q P](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-4.jpg)
Ex 2: The Electric Potential of a Dipole y a -q a +q P Find: a) Potential V at point P. b) What if x>>a ? c) Find E. x
![Solution Solution](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-5.jpg)
Solution
![Ex 3 Find the potential of a finite line charge at P AND the Ex 3: Find the potential of a finite line charge at P, AND the](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-6.jpg)
Ex 3: Find the potential of a finite line charge at P, AND the y-component of the electric field at P. P r d dq x L
![Solution Solution](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-7.jpg)
Solution
![Ex 3 Find the potential of a uniformly charged sphere of radius R inside Ex 3: Find the potential of a uniformly charged sphere of radius R, inside](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-8.jpg)
Ex 3: Find the potential of a uniformly charged sphere of radius R, inside and out. R
![Uniformly Charged Sphere radius R E R r V Uniformly Charged Sphere, radius R E R r V](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-9.jpg)
Uniformly Charged Sphere, radius R E R r V
![Recall that the electric field inside a solid conducting sphere with charge Q on Recall that the electric field inside a solid conducting sphere with charge Q on](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-10.jpg)
Recall that the electric field inside a solid conducting sphere with charge Q on its surface is zero. Outside the sphere the field is the same as the field of a point charge Q (at the center of the sphere). The point charge is the same as the total charge on the sphere. Find the potential inside and outside the sphere. +Q R
![Solution Inside rR E0 integral of zero constant so Vconst Outside rR E Solution -Inside (r<R), E=0, integral of zero = constant, so V=const -Outside (r>R), E](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-11.jpg)
Solution -Inside (r<R), E=0, integral of zero = constant, so V=const -Outside (r>R), E is that of a point charge, integral gives V=k. Q/r
![Solid Conducting Sphere radius R E R r V Solid Conducting Sphere, radius R E R r V](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-12.jpg)
Solid Conducting Sphere, radius R E R r V
![Quiz A charge Q is placed on a spherical conducting shell What is the Quiz A charge +Q is placed on a spherical conducting shell. What is the](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-13.jpg)
Quiz A charge +Q is placed on a spherical conducting shell. What is the potential (relative to infinity) at the centre? A) B) C) D) ke. Q/R 1 ke. Q/R 2 ke. Q/ (R 1 - R 2) zero +Q R 1 R 2
![Calculating V from Sources i Point source note V 0 as r or Calculating V from Sources: i) Point source: (note: V 0 as r ) or](https://slidetodoc.com/presentation_image/7b7cdd3d3a561c9c7172f731bfe5f76d/image-14.jpg)
Calculating V from Sources: i) Point source: (note: V 0 as r ) or ii) Several point sources: (Scalar) iii) Continuous distribution: OR … I. Find from Gauss’s Law (if possible) II. Integrate, (a “line integral”)
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