A capacitor is constructed of two concentric spherical metal shells. The inner s
ID: 1595180 • Letter: A
Question
A capacitor is constructed of two concentric spherical metal shells. The inner shell has a radius R_1 = 15.0 cm, and the outer cylinder has a radius R_2 = 16.0 cm. The hollow space between the two shells is filled with nylon having a dielectric constant of 4.0. A charge of Q = 1mu C is transferred from the inner shell to the outer shell. (a) Find the field between the two using Gauss's law. (b) What is the voltage difference delta V between the inner and outer shells? (c) What is the capacitance C = Q/AV of this spherical capacitor (in pF)?Explanation / Answer
Given; R1 = 0.15 m, R2 = 0.16 m
(a)electric field E = - K*Q/R^2
E1 = - 9.0*10^9*1*10^-6/0.15^2
= -400 K.N/C
E2 = - 9.0*10^9*1*10^-6/0.16^2
= -351.56 K.N/C
(b) The voltage diffrence between the inner and outer shells
delta V = (Q/4*pi*E0)*(1/R2-1/R1)
= 1*10^-6*9*10^9*(1/0.16-1/0.15)
= -3.75*10^3 volts
(c) The capacitance is
C = Q/delta V
= 1*10^-6/3.75*10^3
= -0.267*10^-9 F
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