241-23_Lec-7 - Physics 241 Lecture 7 Y. E. Kim September...

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Physics 241 Lecture 7 Y. E. Kim September 14, 2010 Chapter 23 September 14, 2010 University Physics, Chapter 23 1
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Review - Electric Potential Energy and Electric Potential positive charge High U (potential energy) Low U negative charge High U Low U High V (potential) Low V Electric field direction High V Low V Electric field direction
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University Physics, Chapter 23 September 14, 2010 3 If a charged particle moves perpendicular to electric field lines, no work is done If the work done by the electric field is zero, then the electric potential must be constant Thus equipotential surfaces and lines must always be perpendicular to the electric field lines Review Equipotential Surfaces and Lines V   W e q 0 V is constant 0 if W qE d d E
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University Physics, Chapter 23 September 14, 2010 4 Calculating the Potential from the Field Work dW done on a particle with charge q by a force F over a displacement ds : Work done by the electric force on the particle as it moves in the electric field from some initial point i to some final point f Potential difference: Potential: dW F ds qE ds f i W qE ds  f e fi i W V V V E ds q     (Convention: i = , f = x) () x V x E ds
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University Physics, Chapter 23 September 14, 2010 5 Example: Charge Moves in E field (1) Given the uniform electric field E , find the potential difference V f -V i by moving a test charge q 0 along the path icf, where cf forms a 45º angle with the field. Idea: Integrate along the path connecting i and c, then c and f. (Imagine that we move a test charge q 0 from i to c and then from c to f.)         cf f i f c c i ic V V V V V V E ds E ds      E ds
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University Physics, Chapter 23 September 14, 2010 6 Example: Charge Moves in E field (2) 0 (ds perpendicular to E) cos( ) cf fi ic c i ff cc V V E ds E ds E ds E ds E ds Ed     V V Ed  
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University Physics, Chapter 23 September 14, 2010 7 Electric Potential for a Point Charge (1) We’ll derive the electric potential for a point source q , as a function of distance R from the source That is, V(R) Remember that the electric field from a point charge q at a distance r is given by The direction of the electric field from a point charge is always radial V is a scalar We integrate from distance R (distance from the point charge) along a radial to infinity: 2 ˆ () kq E r r r 2 RR R kq kq kq V E ds dr r r R       
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University Physics, Chapter 23 September 14, 2010 8 Electric Potential for a Point Charge (2) The electric potential V from a point charge q at a distance r is then Positive point charge Negative point charge () kq Vr r
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University Physics, Chapter 23 September 14, 2010 9 Electric Potential from a System of Charges We calculate the electric potential from a system of n point
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This note was uploaded on 11/28/2010 for the course PHY 222 taught by Professor Yu during the Spring '10 term at Beaufort County Community College.

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241-23_Lec-7 - Physics 241 Lecture 7 Y. E. Kim September...

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