110408-opp - (composed by Steve Reich) 4/8/11 Physics 122 1...

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Unformatted text preview: (composed by Steve Reich) 4/8/11 Physics 122 1 Δ ( 1 2 mv 2 )= F net || Δr = F i Δr = W net net − ΔU i = Wi 4/14/10 Physics 122 11 General case ΔU E = − FE ⋅ Δr ( ΔU E = − ∑ FE ⋅ Δr ) (small step) (lots of little steps) finish ΔU E = − ∫ FE ⋅ dr start Simplest case (one source charge, one test charge) finish ΔU E = − ∫ start ⎛1 1⎞ kC qQ dr FE ⋅ dr = − ∫ 2 dr = − kC qQ ∫ 2 = − kC qQ ⎜ − ⎟ r r ⎝ ri rf ⎠ ri ri kC qQ U E (r ) = r 4/8/11 rf rf NOT A VECTOR – JUST A NUMBER Physics 122 13 Field of force felt by a positive test charge near a positive source. Electric Field felt by a positive test charge near a positive source. 4/8/11 kqQ F= 2 r kQ E= 2 r Physics 122 15 Field of force felt by a negative test charge near a positive source. Electric Field felt by a negative test charge near a positive source. 4/8/11 kqQ F= 2 r kQ E= 2 r Physics 122 17 F E= q 4/14/10 U V= q Physics 122 18 Potential energy of a positive test charge near a positive source. Electric Potential of a positive test charge near a positive source. 4/8/11 kqQ U= r kQ V= r Physics 122 19 Potential energy of a positive test charge near a positive source. Electric Potential of a positive test charge near a positive source. 4/8/11 kqQ U= r kQ V= r Physics 122 20 Δ( mv ) = F 1 2 ΔU grav 4/14/10 2 net ⋅ Δr = mg ⋅ Δr = − mg Δh = mg Δh Physics 122 21 ΔU = − F i Δr ΔU F=− Δr (stepping in the direction of the steepest descent) 4/14/10 Physics 122 22 F g= m 4/14/10 Vgrav = Physics 122 U grav m = gh Not equal! 23 r ∞ to r 4/14/10 Physics 122 24 ...
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110408-opp - (composed by Steve Reich) 4/8/11 Physics 122 1...

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