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Chapter 24b

# Chapter 24b - Chapter 24 Electric Potential Part B Electric...

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September 16, 2009 Ch. 24: Electric Potential - Part B 1 Chapter 24: Electric Potential – Part B ! Electric potential energy and potential. ! Calculating the potential from the field. ! Potential due to a point charge. ! Potential due to a group of point charges. ! Potential due to an electric dipole. ! HITT question. ! Potential due to a continuous charge distribution Line of charge. Charged disk.

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September 16, 2009 Ch. 24: Electric Potential - Part B 2 Electric Potential Energy fi UU U W ∆= = If a system of charges changes its configuration from an initial state i to a different final state f , the electrostatic force does work W on the particles. The work done is path independent (conservative force). initial state final state f U i U q 1 q 2 q 3 q 1 q 2 q 3
September 16, 2009 Ch. 24: Electric Potential - Part B 3 Electric Potential ! The electric potential V is the potential energy per unit charge at a point in an electric field. ! The electric potential is a scalar (not a vector). U V q = ! Electric potential difference between two points. fi U VV V q ∆= = UW F d q E d = −⋅ = ! ! ! ! VE d ! !

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September 16, 2009 Ch. 24: Electric Potential - Part B 4 Calculating the Potential from the Field 00 for dW F ds F q E dW q E ds =⋅ = !! ! ! ! We can calculate the potential difference between any two points i and f in an electric field if we know the electric field vector E all along any path connecting those points. ! First we calculate the work done on a positive test charge +q 0 by an arbitrary (nonuniform) electric field E as the charge moves along the path from i to f . ! At any point on the path, an electrostatic force q 0 E acts on the charge as it moves through a differential displacement ds .
September 16, 2009 Ch. 24: Electric Potential - Part B 5 Calculating the Potential from the Field 0 f i Wd W q E d s == ! ! 0 fi W VV V q ∆= = f i E d s −= ! ! ! We find the total work by summing (integrating) the differential works as the charge moves through all the displacements ds along the path. The potential difference between any two points i and f in an electric field is the negative of the line integral (integral along a particular path) of from i to f .

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Chapter 24b - Chapter 24 Electric Potential Part B Electric...

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