A cylindrical capacitor has an inner conductor of radius 2.8 mm and an outer con

Question

A cylindrical capacitor has an inner conductor of radius 2.8 mm and an outer conductor of radius 4.0 mm . The two conductors are separated by vacuum, and the entire capacitor is 2.1 m long. Part A What is the capacitance per unit length? Part B The potential of the inner conductor relative to that of the outer conductor is 350 mV . Find the charge (magnitude and sign) on the inner conductor. Part C The potential of the inner conductor relative to that of the outer conductor is 350 mV . Find the charge (magnitude and sign) on the otter conductor.

Explanation / Answer

(a)

Radius of inner conductor of a cylindrical capacitor= a = 2.8 mm

Radius of outer conductor = b = 4mm .

The two conductors are separated by vacuum.Length of entire capacitor =L= 2.1 m

The capacitance per unit length = C/L= 2pi(eo)/ln(b/a)

The capacitance per unit length = C/L= 55.60619*10^-12/ln(4.0/2.8)

The capacitance per unit length = C/L= 55.60619*10^-12/0.356675

The capacitance per unit length = C/L= 1.556*10^-10 F = 15.56*10-11F

(b)

The potential of the inner conductor relative to that of the outer conductor is 350 mV .

The charge (magnitude and sign) on both conductors= q =CV

q =( 15.56*10-11 )*2.1*0.35

Charge on outer= q = + 1.14366*10^-10 C

Charge on inner= q = - 1.14366*10^-10 C

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