A conducting sphere of radius a = 5cm is surrounded by a dielectric shell, with

Question

A conducting sphere of radius a = 5cm is surrounded by a dielectric shell, with constant dielectric = 5, inner radius b = 10cm, and outer radius c = 15cm. The system is shown to the right. (a)Compute the capacitance between the conductor and ground. Report both the symbolic value and a numeric value. Clearly report and label any intermediate quantities used to get your result and carefully show your work. (b)If the conductor has a potential difference of 100V with the ground, what charge is on the conductor? (c)What is the energy of the system if the potential difference between the inner conductor and ground is 100V?

Explanation / Answer

a) Here are two sperical capacitance in series. Note: I am writing the value in pi epsilon where pi=3.14, epsilon=8.85x10-12,

C1 = 4pi*epsilon ab/(b-a) = 4pi*epsilon *10*5/(10-5) =40 pi epsilon

C2=  4pi*k*epsilon cb/(c-b) =4pi*5*epsilon *10*15/(15-10) = 600 pi epsilon

C1 and C2 are in Series . So C= C1*C2/(c1+c2) = 40*600(40+600) =37.5 pi epsilon

b)Voltage across c1= 100*600/(600+40) =93.75V

Charge on conductor = C1.V1 = 93.75 *37.5 pi epsilon = 3515.625 pi*epsilon

C)energy = 0.5 cv2 =0.5 * 37.5 * pi epsilon* 100*100 =5.2 x10-6 J

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