The space between two concentric conducting spherical shells ofradii b = 1.70 cm

Question

The space between two concentric conducting spherical shells ofradii b = 1.70 cm and a =1.20 cm is filled with a substance of dielectricconstant = 29.5. A potentialdifference V = 65.5 V is applied across the inner and outershells. (a) Determine the capacitance of the device.
nF

(b) Determine the free charge q on the innershell.
nC

(c) Determine the charge q' induced along the surfaceof the inner shell.
nC
(a) Determine the capacitance of the device.
nF

(b) Determine the free charge q on the innershell.
nC

(c) Determine the charge q' induced along the surfaceof the inner shell.
nC

Explanation / Answer

(a)     the capacitance of an air filled sphericalcapacitor is given by     Co = 4 o(a b/ (b - a))          = ......... F (b)      the charge on the positive plate is givenby      q = C V (c)     let the charge on the inner conductor be - qthen adjecent to it is the induced charge q '     as the electric field is less by a factor (1 /k) than the field when no dielectric is present then     - q + q ' = - q / k     q ' = [(k - 1) / k] q          = 4 (k - 1)(a b / (b - a)) V          = ............ C

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