1) Assume a conducting sphere of radius 5 cm is connected to a 1000 V power supp

Question

1) Assume a conducting sphere of radius 5 cm is connected to a 1000 V power supply. What is the charge density on the surface of the sphere in C/m^2?

2) Assume that a proof plane is a conducting disc with a radius of 1.0 cm and is used to transfer some charge from the sphere described above. How much charge will be transferred in one "scoop?"

3) What is the capacitance of two parallel circular plates, each of radius 10 cm, and separated by 1.0 mm?

4) Two capacitors, of capacitance 50 nF and 100 nF, are connected in parallel. This combination is then connected in series to a 200 nF capacitor. What is the total capacitance of the network?

Explanation / Answer

Given radius of the sphere   r = 5 cm potential V = 1000 V    1)            charge density on the surface of the sphere                          s   = charge / surface area = q   / 4pr^2            potential    V = q / 4pe_o r                charge on the surface opf the sphere                     q = 1000 * 4 *3.14 * 8.89* 10^-12 * 5*10^ -2                         = 5.58 nC          therefore    s = 5.58 / ( 4*3.14 * 25*10^ -4 )                                = 0.0177*10^ -5    C /m^2   capacitance of spherical capacitor                 C =  4pe_o r                        =4 *3.14 * 8.89* 10^-12 * 10*10^ -2                     = 0.11 nF   50 nF and   100 nF are in parallel combination                    C = 50 +100 = 150 nF       C and   200 nF in series combination             C_eq   =   150*200 / 200+150 = 8507142 nF  

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