P26_045 - 45. (a) According to Eq. 26-17 the capacitance of...

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Unformatted text preview: 45. (a) According to Eq. 26-17 the capacitance of an air-filled spherical capacitor is given by C0 = 4πε0 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 = 4πκε0 ab . b−a (b) The charge on the positive plate is q = CV = 4πκε0 ab V. b−a (c) Let the charge on the inner conductor to 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, κ−1 ab q= q = 4π (κ − 1)ε0 V. κ b−a ...
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