A cylindrical capacitor has an inner conductor of radius 1.5 mm andan outer conductor of radius 3.4 mm.The two conductors are separated by vacuum, and

beljuA 2021-03-05 Answered

A cylindrical capacitor has an inner conductor of radius 1.5 mm andan outer conductor of radius 3.4 mm.The two conductors are separated by vacuum, and the entire capacitor is 3.0 m long. 
a) What is the capacitance per unit length? 
b)The potential of the inner conductor is 350 mV higher than that of the outer conductor. Find the charge (magnitude and sign) on both conductors. Find the charge (magnitude and sign) on both conductors.

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Expert Answer

Talisha
Answered 2021-03-06 Author has 93 answers
a) Inner radius r1=1.5×103 m
outer radius r2=3.4×103 m
The capacitance of a cylindrical capacitance is given by
C=2πϵ0lln(r2r2)
Cl=2(3.14)(8.854×1012)ln(3.4×103 m1.5×103 m)
=6.80×1011 Fm
(b)
The inner conductor is at a higher potential than the outer conductor it implies that the sign of the charge on the inner conductor is positive outer conductor is negative the magnitude of charge will be same.
The magnitude of charge on each capacitor plate is,
q=(Cl)lvab
=6.80×1011 FM(3.0m)(350×103 V)
=7.14×1011 C
Charge on the outer conductor q=7.14×1011 C
Charge on the inner conductor q=7.14×1011 C

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Jeffrey Jordon
Answered 2021-10-05 Author has 2495 answers

Answer:

Part(a): The capacitance per unit length of the capacitor is

1.56×1010Fm1

Part(b): The charge in the inner shell is +1.6×1010C and the charge of the outer shell is 1.6×1010C

Explanation:

Part(a):

The capacitance (C) per unit length of a cylindrical capacitor is given by

C=2πϵ0log(b/a)

where 'ϵ0' is the permittivity of free space, 'b' is the radius of the outer shell and 'a' is the radius of the inner shell.

Given, b=3.4mm=0.0034 and a=1.5mm=0.0015 mm. We know, ϵ0=8.854×1012Fm1. Substituting the values in the above equation,

C=2π×8.85×1012Fm1log(0.0034/0.0015)=1.56×1010Fm1

Part(b):

As the voltage on the inner conductor is higher than that of the outer conductor, positive charge resides on the inner shell and negative charge resides on the outer shell.

The charge 'Q' of a capacitor of length 'L' having capacitance 'C' and potential difference 'V' is given by

Q=CVL

Given, V=350mV=350×103V and L=3.0m. Substituting these values in the above expression

Q=1.56×1010Fm1×350×103V×3m=1.6×1010C

The charge in the inner shell is +1.6×1010C and the charge of the outer shell is 1.6×1010C.

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