Lecture11 - Physics 132 Introductory Physics: Electricity...

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1 January 30, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 1 Physics 132 Introductory Physics: Electricity and Magnetism Winter Quarter 2008 Lecture 11 January 30, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 2 Examples of Potentials and Fields Point charge : V = Q 4 πε 0 r E = = 4 0 2 Dipole (far away, along axis) : = p 4 0 z 2 = = 2 0 3 Linearly changing potential: = Kz = = K = σ ε 0 +q -q d +q
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2 January 30, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 3 Continuous Charge Distributions Calculating potentials for continuous charge distributions is much like calculating E fields, only simpler. V is a scalar, so there is only one integral to do and no components to worry about. Divide charge into small pieces dq. Treat each as a point charge. Integrate over the object. r dq V at center of ring with charge Q : dq = λ rd φ = Q 2 π r V = dq 4 πε 0 r = 1 4 0 = 4 0 d 0 2 = 1 4 0 Q 2 (2 ) = 4 0 January 30, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 4 Potential of a Cut Ring What is the potential due to a partial ring of charge covering a 300 ° angle? The total charge is -5Q. Compute the potential on the axis of the ring. R z The ring has a 60 ° gap, so it is 5/6 complete. It can be modeled as a superposition of a -6Q complete ring and a +1Q segment spanning 60 ° . All charge is the same distance from a point on the z-axis. = k ( 6 ) R 2 + z 2 = 5 kQ 2 + 2
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3 January 30, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 5 Potential for a Hollow Sphere r r E V 1/r 2 1/r What is the potential for a hollow spherical shell of radius R with charge +Q? Outside-same as a point charge +Q at the origin. Inside- E=0 so V is constant. V ( r ) = Q 4 πε 0 > R ( ) = 4 0 < January 30, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 6 Calculating the Potential: Step-by-step 1) Make a good sketch, define your variables, and label the quantities you’ll need in the calculation. Choose a way to
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Lecture11 - Physics 132 Introductory Physics: Electricity...

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