Chapter 2: Q43P (page 107)

Find the capacitance per unit length of two coaxial metal cylindrical tubes, of radi $^{a}$ and $^{b}$ .

Short Answer

Expert verified

The capacitance per unit length is $^{\frac{C}{I} = \frac{2 π ε_{0}}{I n (\frac{b}{a})}}$

Step by step solution

Determine the expression for the electric field.

Write the expression for electric filed,

$E = \frac{q}{2 π s I ε_{0}} \hat{s} f o r a < s < b$

Here, $^{q}$ is the charge, $^{E}$ is the electric filed.

Consider the given figure.

Now consider $^{I}$ is the length of the tube.

Let’s give the chargelocalid="1654330497372" $^{+ q}$ to the inner cylinder and $^{- q}$ to the outer cylinder.

Determine the expression for potential difference

Now finding the potential difference between inner and outer faces of cylinder and it is given by,

$V (a) - V (b) = - \int_{b}^{a} (\frac{q}{2 π s I ε_{0}}) d s V (a) - V (b) = V$

Solve further as,

$V = - \int_{b}^{a} (\frac{q}{2 π s I ε_{0}}) d s = - \frac{q}{2 π ε_{0} I} (\log a - \log b) = \frac{q}{2 π ε_{0} I} I n (\frac{b}{a})$

Determine Capacitance per unit length

$\frac{C}{I} = \frac{2 π ε_{0}}{I n (\frac{b}{a})}$ Consider the expression for the potential.

Now comparing the above equation with localid="1654328482139" $V \frac{q}{C}$ , here $^{C}$ is the capacitance. Then,

localid="1654328603077" $\frac{C}{I} = \frac{2 π ε_{0}}{I n (\frac{b}{a})}$

$^{\frac{C}{I} = \frac{2 π ε_{0}}{I n (\frac{b}{a})}}$

Hence, the capacitance per unit length is given by,

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find the capacitance per unit length of two coaxial metal cylindrical tubes, of radi $^{a}$ and $^{b}$ .

Short Answer

Step by step solution

Determine the expression for the electric field.

Determine the expression for potential difference

Determine Capacitance per unit length

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

Engineering Physics

Electrostatics

Geometrical and Physical Optics

Fields in Physics

Thermodynamics

Study anywhere. Anytime. Across all devices.

Find the capacitance per unit length of two coaxial metal cylindrical tubes, of radiaandb.

Short Answer

Step by step solution

Determine the expression for the electric field.

Determine the expression for potential difference

Determine Capacitance per unit length

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

Engineering Physics

Electrostatics

Geometrical and Physical Optics

Fields in Physics

Thermodynamics

Study anywhere. Anytime. Across all devices.

Find the capacitance per unit length of two coaxial metal cylindrical tubes, of radi $^{a}$ and $^{b}$ .