a) A capacitor consisting of two concentric spheres of radius R 1 and R 2 = 2.00

Question

a) A capacitor consisting of two concentric spheres of radius R1 and R2 = 2.00·R1 has a capacitance of C = 6.00 picoFarads and is charged to a potential difference of 66.0 Volts. Calculate the energy stored in the capacitor.

Answer-1.31E-8 J

b) Calculate the charge on this capacitor, when the electrical energy stored is 29.4·10-8 Joules.

Answer- 1.88E-9

c) If the radius of the outer sphere is increased by a factor of 3.00 while keeping the charge on the plates constant, by what factor does the stored energy change?

Answer- ?

Hint: Calculate the capacitance of a sphere in terms of R1 before and after R2 was increased. By considering the ratio of the two stored energies, the unknown radius, R1, drops out. Use the energy formula containing charge.

****I need help with part c**** Step by step if possible

Explanation / Answer

c) Capacitance of spherical concentric sphere = 4*pi*epsilon ( R1 R2) / (R2 - R1)

q is constant

Case 1: R2 = 2 R1

Case 2: R2 = 6R1

E = q2 / 2C

=> E2 : E1 = C1:C2 (since q is same)

= (R1 * 2R1)(6R1 - R1) / (2R1 - R1) (R1 * 6R1)

= 2*5 / (1*6) = 10/6 = 1.667

So stored energy increases to a factor of 1.667

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