Question

A spherical capacitor contains a solid spherical conductor of radius 1 mm, surrounded by a dielectric material with &r 2.0 out to a radius of 2 mm, then an outer thin spherical conducting shell. Determine the capacitance of the spherical capacitor. (Hint: Suppose you place a charge Q on the inner conductor and a charge -0 on the outer conductor Determine the electric field in the dielectric region between the conductors, then integrate SE .dr to determine the vollage difference between the conductors, and using the charge and the voltage determine the capacitance of the spherical capacitor.) 4)

Answer 1

Formula for spherical capacitor is capacitance = (4 pi K E/1/r_i - 1/r_o) where k = relative permittivity E = permittivity of space r i = inner radius r_o = outer radius as per question given implies E_r = 2.0 r_i = 1 m r_o = 2m where epsilon = e_e_o e = 2.0 times 8. 854 times 10^-12 F/m Epsilon = 17. 708 times 10^-12 F/m put all above given values in above formula capacitance implies 4 piK E/ 1/ r_i - 1/r_o) implies 4 pi k (epsilon_r epsilon_o)/ (1/ 1 mm - 1 2 mm) \r\n capacitance 4 pi k times 17. 708 times 10^-12 (F/m)/(10^3/2) (1/m) implies 4 pi k times 17. 708 times 10^-12 F/ (2 times 10^3 - 10^3/2) implies 4 pi k times 17. 708 times 10^-12 F/ (10^3 times 1/2) F/10^+ 3 implies k 445. 050582 times 10^-12/10^3 F implies 445. 050581 k times 10^-15 F