Part A Constants A cylindrical capacitor has an inner conductor of radius 2.6 mm

Question

Part A Constants A cylindrical capacitor has an inner conductor of radius 2.6 mm and an outer conductor of radius 3.3 IIII . The two conductors are separated by vacuum, and the entire capacitor is 2.2 m long. What is the capacitance per unit length? LG Aep 1 O 2 ? ON pF/m Submit Request Answer Part B The potential of the inner conductor relative to that of the outer conductor is 360 mV . Find the charge (magnitude and sign) on the inner conductor. Express your answer with the appropriate units. CPH HÅ + O 2 ? Q - Value Units Submit Request Answer Part C The potential of the inner conductor relative to that of the outer conductor is 360 mV . Find the charge (magnitude and sign) on the otter conductor. Express your answer with the appropriate units.

Explanation / Answer

Given

cylindrical capacitot with inner radius is a = 2.6 mm

outer radius b = 3.3 mm

length of the capacitor is l = 2.2 m

Part A

capacitance per unit length is C/l = ?

we know that the capacitance is  

C = (2pi*epsilonnot*l)/ln(b/a)

now C/l = (2pi*epsilonnot*l)/ln(b/a)

= (2pi*epsilonnot)/ln(b/a)

substituting the values  

= (2pi*8.854*10^-12)/ln(3.3/2.6) F

= 1.3263121 *10^-11 F  

C/l = 1.3263121*10^-11 F

PArtB

potential of inner conductor is 360 mV relative to the outer conductor so

the inner conductor is +ve charged and outer one is -ve charged

we know that the charge on each plate is same in a conductor s

charge q = (C/l)l*V

q = (1.3263121*10^-11)(2.2)*360*10^-3 C

q = 10.5044*10^-12 C

so the inner conductor charge is q = +10.5044*10^-12 C

outer conductor charge is q = - 10.5044*10^-12 C

Part C

the outer conductor is at potential is 360 mV relative to inner conductor that is  

the outer conductor is at higher potential than inner conductor

charge q = (C/l)l*V

q = (1.3263121*10^-11)(2.2)*360*10^-3 C

q = 10.5044*10^-12 C

outer conductor charge is q = + 10.5044*10^-12 C

the inner conductor charge is q = -10.5044*10^-12 C

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