A capacitor consisting of two concentric spheres of radius R1 and R2 2.00-R1 has

Question

A capacitor consisting of two concentric spheres of radius R1 and R2 2.00-R1 has a capacitance of C4.00 picoFarads and is charged to a potential difference of 74.0 Volts. Calculate the energy stored in the capacitor. Calculate the charge on this capacitor, when the electrical energy stored is 20.410 8 Joules. Seomit Anses Tries 0/12 If the radius of the outer sphere is Increased by a factor of 4.50 while keeping the charge on the plates constant, by what factor does the stored energy chanqe? Siet Anane Tries 0/12 Post Discussion 4 Send Feedback

Explanation / Answer

capacitance C0 = 4*pi*e0*/(1/R1 - 1/R2) = 4*pi*e0/(1/R1 - 1/(2R1))

C0 = 8*pi*e0*R1 = 4*10^-12 F

energy stored in capacitor U = (1/2)*C*V^2

U = (1/2)*4*10^-12*74^2 = 1.1*10^-8 J

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energy E == (1/2)*Q^2/C

20.4*10^-8 = (1/2)*Q^2/(4*10^-12)

Q = 1.28*10^-9 C

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Capacitance C = 4*pi*e0/(1/R1 - 1/4.5R1) = 0.78*4*pi*e0*R1

C = 0.78*c0/2 = 0.78*2*10^-12 = 0.39*10^-12 F

energy stored E = (1/2)*Q^2/C = (1/2)*(1.28*10^-9)^2/(0.39*10^-12)

E = 2.1*10^-6 J

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