A capacitor consistingof two concentric spheres of radius R 1 and R 2 = 3.50·R 1

Question

A capacitor consistingof two concentric spheres of radius R1 and R2= 3.50·R1 has a capacitance of C = 8.00picoFarads and is charged to a potential difference of 88.0Volts.

a-Calculate the energy stored in the capacitor.

b-Calculate the charge on this capacitor, whenthe electrical energy stored is 32.3·10-8Joules.

If the radius of the outer sphere isincreased by a factor of 5.00 while keeping the charge on theplates constant, by what factor does the stored energy change?
Hint:
Calculate the capacitance of a sphere in terms of R1 before andafter R2 was increased. By considering the ratio of the two storedenergies, the unknown radius, R1, drops out. Use the energy formulacontaining charge. Calculate the capacitance of a sphere in terms of R1 before andafter R2 was increased. By considering the ratio of the two storedenergies, the unknown radius, R1, drops out. Use the energy formulacontaining charge.

Explanation / Answer

c) C = 4o(R1R2/ R2-R1) =4o (3.50R1/ 2.5) =1.4R1 * 4o        If R2 = 17.5 R1     ==> C' = 4o(17.5R12/ 16.5R1)                 = 1.066R1 *4o   ==> C / C' = 1.4/ 1.066 We know that                   U = 0.5 CV2           U /U'   = C / C' = 1.4 / 1.066 = 1.313

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