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3. For the following geometry, if the potential applied between the two conductive plates is Vo, find the total capacitance? Does the Ctotal follow the capacitance of two capacitors in series or in parallel? d P1s -P1s + + + + €₁ + P2s E₂ -P2s + €2 Vo

3. For the following geometry, if the potential applied between the two conductive plates is Vo, find the total capacitance? Does the Ctotal follow the capacitance of two capacitors in series or in parallel? d P1s -P1s + + + + €₁ + P2s E₂ -P2s + €2 Vo

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3. For the following geometry, if the potential applied between the two conductive plates is Vo, find the total capacitance? Does the Ctotal follow the capacitance of two capacitors in series or in parallel? Pis -P1s + €₁ + + + + E₂ P2s -P2s + €2 + Vo
Transcribed Image Text:3. For the following geometry, if the potential applied between the two conductive plates is Vo, find the total capacitance? Does the Ctotal follow the capacitance of two capacitors in series or in parallel? Pis -P1s + €₁ + + + + E₂ P2s -P2s + €2 + Vo
2. a. In class we had this slide that was not complete: HW b V E V²V = 10 r² or 10 av dr Since the dielectric is homogeneous, the symmetry of this problem implies that V only varies with r: Thus, Laplace's equation becomes: av 1 d sin 8. r² sine de ᎧᎾ . => V(r) = A 1² OV) = = 0 =>7² -= A => OV = = 4/ôr =>V=-=+B or >p²OV. 2 dr applying the boundary conditions: V(r= a)=-- =A+B=V₁ a V(r=b)=+B=0 =4+ Vo (5) 550 b (1. a b a A = Vo b a -(for:a<r<b) 1 8²v =0 r² sin² 0 dp² 7 B A b V₂ r 1 b(-- b a V₂ (1. b HW: Using the expression we found for V find: E, D, P, Q, C Find E, D and the surface charges o and the Capacitance C Using: 1. The Laplace eq method and 2. The Gauss's law method assuming the inner sphere has a total charge of +Q on it. b. Find the Capacitance for an isolated sphere (hint: use the equation you found for C in part a for when the outer sphere has an infinite radius).
Transcribed Image Text:2. a. In class we had this slide that was not complete: HW b V E V²V = 10 r² or 10 av dr Since the dielectric is homogeneous, the symmetry of this problem implies that V only varies with r: Thus, Laplace's equation becomes: av 1 d sin 8. r² sine de ᎧᎾ . => V(r) = A 1² OV) = = 0 =>7² -= A => OV = = 4/ôr =>V=-=+B or >p²OV. 2 dr applying the boundary conditions: V(r= a)=-- =A+B=V₁ a V(r=b)=+B=0 =4+ Vo (5) 550 b (1. a b a A = Vo b a -(for:a<r<b) 1 8²v =0 r² sin² 0 dp² 7 B A b V₂ r 1 b(-- b a V₂ (1. b HW: Using the expression we found for V find: E, D, P, Q, C Find E, D and the surface charges o and the Capacitance C Using: 1. The Laplace eq method and 2. The Gauss's law method assuming the inner sphere has a total charge of +Q on it. b. Find the Capacitance for an isolated sphere (hint: use the equation you found for C in part a for when the outer sphere has an infinite radius).
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