W9_parallel_resonance.eps
Week 4: Capacitance 139 the result can be shown to hold in the more general case of varying fields using more calculus in a late ...
140 Week 4: Capacitance +Q −Q C 1 C 2 C 3 Ctot Vtot 1 +Q −Q +Q −Q V V 2 V 3 +Q −Q Figure 42: Find the total capacitance of a muc ...
Week 4: Capacitance 141 have been any number! We just add the potentials across as many as we have (with the same charge on each ...
142 Week 4: Capacitance This makes the problem of finding the total capacitance really easy! Qtot = Q 1 +Q 2 +Q 3 +... CtotV = C ...
Week 4: Capacitance 143 We still don’t knowallof Maxwell’s equations, but when we do, we will be forced to confrontthe unpleasan ...
144 Week 4: Capacitance in a ball of radiusais (see above or better yet, use Gauss’s Law to derive it again for yourself): Eatom ...
Week 4: Capacitance 145 Dielectric Response of an Insulator in an Electric Field Now that we understand whateachatom in an insul ...
146 Week 4: Capacitance charge. We will only consider boundsurfacechargeσbin this course as the most common important case, but ...
Week 4: Capacitance 147 Now let’s imagine this figure redrawn on a length scale where atoms aretiny– too small to be seen in the ...
148 Week 4: Capacitance This form proves to be most useful in the more advanced treatments of electrodynamics that e.g. physics ...
Week 4: Capacitance 149 that depends only on the free charge and never on the dielectrics present, it will make the more mathema ...
150 Week 4: Capacitance Now just lay down one sheet of foil on the table. Cover it (symmetrically) with the paper. Top it with t ...
Week 4: Capacitance 151 + + + + + + + + + + + + + + + + + + + + + + + + +σ −σ −σb +σbf f E = E / 0 εr Figure 48: Bound and free ...
152 Week 4: Capacitance a function of coordinates. This latter derivation has the advantage in that the first two lines hold for ...
Week 4: Capacitance 153 The last important relation involving bound charge is well beyond the scope of this course to discuss, b ...
154 Week 4: Capacitance Homework for Week 4 Problem 1. Physics Concepts Make this week’s physics concepts summary as you work al ...
Week 4: Capacitance 155 Problem 4. Find the capacitance of the following arrangements: b a c A A d d where the first two are par ...
156 Week 4: Capacitance Problem 7. You are given a square parallel plate capacitor of sideLand plate separationdand a slab of di ...
Week 5: Resistance 157 Advanced Problem 8. You are given a square parallel plate capacitor of sideLand plate separationdand a sl ...
158 Week 5: Resistance ...
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