ch25-p053

# ch25-p053 - 53. (a) According to Eq. 25-17 the capacitance...

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Unformatted text preview: 53. (a) According to Eq. 25-17 the capacitance of an air-filled spherical capacitor is given by ⎛ ab ⎞ C0 = 4πε 0 ⎜ ⎟. ⎝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 23.5 (0.0120 m)(0.0170 m) ⎛ ab ⎞ C = 4πκε 0 ⎜ ⋅ = 0.107 nF. ⎟= 9 2 2 ⎝ b − a ⎠ 8.99 ×10 N ⋅ m C 0.0170 m − 0.0120 m (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 ⎛ 23.5 − 1.00 ⎞ q = 4π (κ −1) ε 0 V =⎜ ⎟ (7.79 nC) = 7.45 nC. κ b−a ⎝ 23.5 ⎠ ...
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