A cylindrical capacitor has an inner conductor with a radius of 1.4mm and an out

Question

A cylindrical capacitor has an inner conductor with a radius of 1.4mm and an outer conductor with a radius of 3.9mm . The two conductors are separated by vacuum, and the entire capacitor has a length of 2.8m .

1- What is the capacitance per unit length?

Express your answer using two significant figures.

2- The potential of the inner conductor relative to that of the outer conductor is 300mV . Find the charge (magnitude and sign) on both conductors.

Enter your answers numerically separated by a comma. Express your answers using two significant figures.

Explanation / Answer

Radius of inner conductor of a cylindrical capacitor= a = 1.4mm

Radius of outer conductor = b = 3.9mm .

The two conductors are separated by vacuum.Length of entire capacitor =L= 2.8 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(3.9/1.4)

The capacitance per unit length = C/L= 55.60619*10^-12/1.024
The capacitance per unit length = C/L= 54.3029 *10^-12 F
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b) The potential of the inner conductor relative to that of the outer conductor is 300 mV .

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

q =( 54.3029 *10^-12 )*2.8*0.30

Charge on outer= q = + 4.56144*10^-11 C

Charge on inner= q = - 4.56144*10^-11 C

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