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Unformatted text preview: 47. (a) According to Eq. 25-17 the capacitance of an air-filled spherical capacitor is given by
C0 = 4πε 0 ab . b−a When the dielectric is inserted between the plates the capacitance is greater by a factor of the dielectric constant κ. Consequently, the new capacitance is
C = 4πκε 0 23.5 (0.0120)(0.0170) ab = = 0.107 nF. b − a 8.99 ×109 0.0170 − 0.0120 (b) The charge on the positive plate is
q = CV = (0.107 nF)(73.0 V) = 7.79 nC. (c) Let the charge on the inner conductor be –q. Immediately adjacent to it is the induced charge q'. Since the electric field is less by a factor 1/κ than the field when no dielectric is present, then –q + q' = –q/κ. Thus, q′ = = κ −1 ab q = 4π (κ −1) ε 0 V κ b−a
23.5 − 1.00 (7.79 nC) = 7.45 nC. 23.5 ...
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- Spring '10