Lec08-1 - ture 8-1 ture Electric Potential Energy of a...

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cture 8- cture 8- 1 Electric Potential Energy of a Charge (continued) 0 ( ) ( ) r i U U r U i q E dl = - = - v v u vv g i is “the” reference point . Choice of reference point (or point of zero potential energy ) is arbitrary. 0 dl r i is often chosen to be infinitely far ( ) = l d E q dW 0 - = - = l d E q dW dU 0 - = r i l d E q 0
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cture 8- cture 8- 2 Electric Potential So U( r )/q 0 is independent of q 0 , allowing us to introduce electric potential V independent of q 0 . 0 ( ) ( ) U r V r q r r [Electric potential] = [energy]/[charge] SI units: J/C = V (volts) U( r ) of a test charge q 0 in electric field generated by other source charges is proportional to q 0 . 0 ( ) ( ) U r V r q r r taking the same reference point Potential energy difference when 1 C of charge is moved between points of potential difference 1 V 1 J = Scalar!
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cture 8- cture 8- 3 Two Ways to Calculate Potential Integrate - E from the reference point (∞) to the point ( P ) of observation: ( 29 P V r E dl ∞→ = - r ur r g Integrate dV (contribution to V(r) from each infinitesimal source charge dq ) over all source charges: A line integral (which could be tricky to do) If E is known and simple and a simple path can be used, it may be reduced to a simple, ordinary 1D integral. q 1 q 2 q 3 q 4 P Q P r P Q
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cture 8- cture 8- 4 Equipotential Surfaces An equipotential surface is a surface on which the potential is the same everywhere. 0 0 U V q = = For a displacement Δr of a test charge q 0 along an equipotentital , 0 0 E E q U W r - =- = ∆ = ur r g U = constant on an equipotential surface. E is everywhere perpendictular to U V E r E r ∆ = - ∆ = ∆ ur r ur r g Potential difference between nearby equipotentials is approximately equal to E times the separation distance. Equipotential surfaces are drawn at constant intervals of ΔV http://www.its.caltech.edu/~phys1/java/phys1/EField/EField.html r E q - 0 | | r E -
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cture 8- 5 Potential and Conductors Entire conductor including its surface(s) has uniform V . Equipotential surfaces Draw equipotential surfaces outside the conductor on which V is uniform. 0 E dl
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Lec08-1 - ture 8-1 ture Electric Potential Energy of a...

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