W9_parallel_resonance.eps
Week 2: Continuous Charge and Gauss’s Law 99 Problem 9. a b c −Q 0 +Q 0 Consider three “thin” concentric conducting spherical sh ...
100 Week 2: Continuous Charge and Gauss’s Law Problem 10. R λ The electric field vanishes inside a uniform spherical shell of ch ...
Week 2: Continuous Charge and Gauss’s Law 101 b R ρ 0 b) Material is removed from the sphere to create a spherical cavity of rad ...
102 Week 2: Continuous Charge and Gauss’s Law Advanced Problem 12. x y ∆x ∆y ∆z (x 0 ,y 0 ,z 0 ) z Consider asmallgaussian surfa ...
Week 3: Potential Energy and Potential 103 Note well, to get this result you need to eliminate certain componentsin the full exp ...
104 Week 3: Potential Energy and Potential ...
Week 3: Potential Energy and Potential The change in electrostatic potential energy moving a charge between two points in the f ...
106 Week 3: Potential Energy and Potential withV 0 and arbitrary constant of integration, used to set a suitable zeroof the pote ...
Week 3: Potential Energy and Potential 107 (so thatU 0 is zero, if you prefer). We remain free to choose a different zero, howev ...
108 Week 3: Potential Energy and Potential wherer=|~x|. Alternatively we could use the definition of the field relative to the f ...
Week 3: Potential Energy and Potential 109 that is large enough to contain sufficient charge for a smooth average charge density ...
110 Week 3: Potential Energy and Potential 3.4: Examples of Computing the Potential Example 3.4.1: Potential of a Dipole on thex ...
Week 3: Potential Energy and Potential 111 Now we can differentiate: Ez = − d dz keq (x^2 + (a−z)^2 )^1 /^2 + d dz keq (x^2 + (a ...
112 Week 3: Potential Energy and Potential Example 3.4.2: Potential of a Dipole at an Arbitrary Point in Space +q −q z x +a −a r ...
Week 3: Potential Energy and Potential 113 the denominator to the numerator (losing the square roots in the process). That is: r ...
114 Week 3: Potential Energy and Potential Example 3.4.3: A ring of charge dθ z r a dl = a dθ λ x y Figure 30: A ring of charge ...
Week 3: Potential Energy and Potential 115 Let’s step through this. dl=a dθ (164) defines a differential chunk of the ring. Its ...
116 Week 3: Potential Energy and Potential Q r r R S(outer) S(inner) Figure 31: A spherical shell of charge of radiusR. Example ...
Week 3: Potential Energy and Potential 117 A spherical shell of charge thus produces a potentialoutsidethat looks like the poten ...
118 Week 3: Potential Energy and Potential We integrate both sides, the right hand side over the entire solid angle: V= ∫ dV= ∫ ...
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