# Lec08-1 - Lecture 8-1 Electric Potential Energy of a Charge...

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Lecture 8-1 Electric Potential Energy of a Charge (continued) 0 ( ) ( ) r i U U r U i q E dl i is “the” reference point . Choice of reference point (or point of zero potential energy ) is arbitrary. 0 dl i is often chosen to be infinitely far ( ) l d E q dW 0 l d E q dU 0 r i l d E q 0

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Lecture 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 () Ur Vr q [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 q 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!
Lecture 8-3 Two Ways to Calculate Potential • Integrate - E from the reference point (∞) to the point ( P ) of observation: P V r E dl • 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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Lecture 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 E UW U = constant on an equipotential surface. E is everywhere perpendictular to U V E r 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
Lecture 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 For Δ l on equipotential, or equipotential surface 0 V E l

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Lecture 8-6 Electrostatic Potential Energy of Conductors bring dq in from ∞ q+dq, v +d v v kq U W dq dq R Spherical conductor q, v R Total work to build charge from 0 up to Q: 2 0 1 22 Q kq kQ U U dq QV RR q v dq U Q V kq v r
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## This note was uploaded on 04/23/2011 for the course PHYS 241 taught by Professor Wei during the Spring '08 term at Purdue University.

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Lec08-1 - Lecture 8-1 Electric Potential Energy of a Charge...

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