L12_Viet_Calculating E from V

L12_Viet_Calculating E from V - Physics 122 Electricity and...

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Unformatted text preview: Physics 122 Electricity and Magnetism Lecture 12 Calculating E from V 05/11/09 Physics 122 - Lecture 12 2 Summary 05/11/09 Physics 122 - Lecture 12 3 Summary (2) 05/11/09 Physics 122 - Lecture 12 4 The Missing Link How are E and V connected? 05/11/09 Physics 122 - Lecture 12 5 Finding V from E q+sources U V q V ( ) ; / ; / f i s s s s s U W i f F ds V U q E F q ∆ = - = - ∆ = ∆ = ( ) ( ) f i s f i s s V V S V S E ds ∆ =- = - (uniform electric field) s V E s ∆ = - ∆ 05/11/09 Physics 122 - Lecture 12 6 Potential from the Field of a Point Charge 2 ( ) ( ) 1 4 r r r V V V r q E dr dr r πε ∆ =- = - = - 2 1 ( ) ( ) 4 1 4 1 4 r r q V r V dr r q r q r πε πε πε = + = +- = This is the same result that we obtained earlier from energy considerations. 05/11/09 Physics 122 - Lecture 12 7 Example : The Potential of a Charged Disk disk 2 2 2 disk In Chapter 26, we found that the field on the axis of a charged disk was: 1 2 Find the corresponding potential . Q z E R z R V π ε =- + ( 29 2 2 2 2 2 2 2 2 2 2 2 disk 2 ( ) ( ) ( ) 1 2 2 2 This is the same expression we previously calculated. 2 z z z z z z Q z V z V E z dz dz R z R Q zdz Q dz z z R R R z R Q V z R z R π ε π ε π ε π ε = + = +- + & =- =- + & & + = +- 05/11/09 Physics 122 - Lecture 12 8 Finding E from V q+sources s U W V E s q q ∆- ∆ = = = - ∆ lim s s V dV E s ds ∆ ∆ ∴ = - =- ∆ ; ; x y z dV dV dV E E E dx dy dz = - = - = - ˆ ˆ ˆ dV dV dV E i j k dx dy dz = - + + r In other words, the E field components are determined by how much the potential V changes in the three coordinate directions. 2 1 1 For a point charge: 4 4 r dV d q q E E dr dr r r πε πε = = - = - = 05/11/09 Physics 122 - Lecture 12 9 Example : The E Field of a Charged Ring ring 2 2 ring In Chapter 29, we found that the potential on the axis of a charged ring was: 1 4 Find the corresponding electric field ....
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This note was uploaded on 04/25/2009 for the course E PHYSIS122 taught by Professor Viet during the Spring '09 term at 東京大学.

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L12_Viet_Calculating E from V - Physics 122 Electricity and...

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