Capacitance  Problem 7:   Consider a spherical metal shell of radius R in empty space.  Part (b)  Calculate the capacitance, in picofarads, of such a conductor with a radius of R = 0.058 m.

(a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength of dry air, which is 3.00106 V/m, if the plates are separated by 2.00 mm and a potential difference of 5.010V is applied? (b) How close together can the plates be with this applied voltage?

For the arrangement of capacitors in problem 10, find the equivalent capacitance in μF (microfarads) using C1 = 29.9 μF (microfarads) , C2 = (0.500) C1, and C3 = (0.400) C1 (Answer in 5 sig. figs.)

Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae Trao + B/r + bo where alpha (a), beta (ß), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference ab between the two conductors. The potential difference is related to the electric field by: Vob = - S *Edr= - ["Edr Calculating the antiderivative or indefinite integral, Vab = (-aage" o-r/ao + B + bo By definition, the capacitance C is related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q/( (erb/ao - eralao) + ß In( ) + bo ( ))