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Agenda Today Continuous Charge Distribution Tuesday – lab 5 & Quiz Wed&Fri – Chapter 24 Today –Continuous Charge Distribution Gravity Equivalent Complex Layers HMWK CH. 22 Up Today HMWK Due Thurs.
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Fields & Potential In a Solid Gravity First Earth M=M E R=R E V=(4/3) R E 3 SA=4 R E 2 =M/V=3M E /(4 r E 3 ) Even Distribution? Solid Objects Density Volume Surface Area Mass Electrical Objects Charge & Charge Density
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Find the Zeroes Use reference 0 at infinity (Usual) Earth M=M E R=R E V=(4/3) R E 3 SA=4 R E 2 =M/V=3M E /(4 r E 3 ) Even Distribution Where is F G =0? Where is PE G = 0?
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Gauss’s Law Field then Force? Earth M=M E R=R E V=(4/3) R E 3 SA=4 R E 2 =M/V=3M E /(4 r E 3 ) Even Distribution Flux = Field x Area = EA
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Gauss’s Law Field at a point r? Earth M=M E R=R E V=(4/3) R E 3 SA=4 R E 2 =M/V=3M E /(4 r E 3 ) Even Distribution Choose Surface so E Perp to it. Also, E constant across surface For point charge/sphere Sphere
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Gauss’s Law Field at a point r? Earth M=M E R=R E V=(4/3) R E 3 SA=4 R E 2 =M/V=3M E /(4 r E 3 ) Even Distribution What if “Surface” inside Earth? What is m in equation?
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Gauss’s Law Field at a point r? Earth M=M E R=R E V=(4/3) R E 3 SA=4 R E 2 =M/V=3M E /(4 r E 3 ) Even Distribution What if “Surface” inside Earth? What is m in equation?
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Gauss’s Law Field at a point r? Earth M=M E R=R E V=(4/3) R E 3 SA=4 R E 2 =M/V=3M E /(4 r E 3 ) Even Distribution V encl =(4/3) r 3
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Gauss’s Law Field at a point r? Earth M=M E R=R E V=(4/3) R E 3 SA=4 R E 2 =M/V=3M E /(4 r E 3 ) Even Distribution
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Where (r) is field zero? Earth M=M E R=R E V=(4/3) R E 3 SA=4 R E 2 =M/V=3M E /(4 r E 3 ) Even Distribution
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Where (r) is field zero? Inside: E=Gr(M E /r E 3 ) Outside: E=GM E /r 2 Two Situations Where is “Special Point” Where r = r E Both must have same value Works: Both E=GM E /r E 2 Inside zero: at center of earth Gravitational pull cancels out Outside only zero at infinity Case similar for small - q & big + q What can be different for Elect? Material Dependence!
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Interesting Graph 3D Charge Distribution E r r r=r E Linear Inside 1/r 2 outside Discontinuity Value Same
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What if charged conductor? Metal Charge = +Q Where is field zero? Everywhere inside metal Outside, E=kQ/r 2 Outside is just air + + + + + + + + + + + + + + + + + + + + + + + + +
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Interesting Graph 3D Metal E r r r=r E Zero Inside 1/r 2 outside Discontinuity Value Not Same?
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Real Graph 3D Metal E r r r=r E Zero Inside 1/r 2 outside Discontinuity Value Same Exponential Decay Near Surface NanoScale
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Potential of Charged Conductor? Metal Charge = +Q R=r E, etc.. What is potential in a metal? Constant Where can we find a value? At edge, r=r E V=kQ/r outside V=kQ/r E at edge V=kQ/r E throughout Outside is just air + + + + + + + + + + + + + + + + + + + + + + + + +
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Interesting Graph 3D Metal V r r r=r E Constant Inside 1/r outside Discontinuity Value Same
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What if charged Insulator? Insulator Charge = +Q =1 R=R E, etc… Where is field zero? At center & Infinity Outside, E=kQ/r 2 Inside, E=(k/ )(Qr/r E 3 ) See can make life interesting For now, = 1. E=(k)(Qr/r E 3 ) Outside is just air [ = 1] + + + + + + + + + + + + + + + + + + + + + + + + +
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Interesting Graph 3D Insulating Charge E r r r=r E Linear Inside 1/r 2 outside Discontinuity Value Same What if >1?
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Interesting Graph 3D Insulating Charge E r r r=r E Linear Inside 1/r 2 outside Discontinuity Value Not Same? What if >1? Field becomes smaller inside
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Interesting Graph 3D Insulating Charge E r r r=r E Linear Inside 1/r 2 outside Discontinuity Value Always Same! What if >1? Field becomes smaller inside In transition region from inside to outside, k changes value. Exponential Bridge
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What if charged Insulator? Potential, = 1 Insulator Charge = +Q =1 R=R E, etc… Outside is just air [ = 1] + + + + + + + + + + + + + + + + + + + + + + + + +
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Potential Graph 3D Insulating Charge V r r r=r E Quadratic 1/r outside Discontinuity Value Always Same! What if >1?
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What now? Metal Shell Insulator Charge = +Q =1 R=R E, etc… Outside is just air [ = 1] + + + + + + + + + + + + + + + + + + + + + + + + +
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What now? Metal Shell Insulator Charge = +Q =1 R=R E, etc… Outside is just air [ = 1] + + + + + + + + + + + + + + + + + + + + + + + + + What does charge On shell look like?
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What now? Metal Shell Insulator Charge = +Q =1 R=R E, etc… Outside is just air [ = 1] + + + + + + + + + + + + + + + + + + + + + + + + + What does charge On shell look like? - - - - - - - - - - + + + + + + + +
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Metal Shell Insulator Charge = +Q =1 R=R E, etc… + + + + + + + + + + + + + + + + + + + + + + + + + How much –q on shell? |+q|=|-q|=Q - - - - - - - - - - + + + + + + + + E = 0 in shell E=Q encl /A E=0 Q encl =0
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Agenda Today Continuous Charge Distribution Tuesday – lab 5 & Quiz Wed&Fri – Chapter 24 Today –Continuous Charge Distribution (if Time) Gravity Equivalent Complex Layers HMWK CH. 22 Up Today HMWK Due Thurs.
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