Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 11

The plates of a parallel plate capacitor are of area \(A\), distance apart \(x\) and are at a potential difference \(V\). A slab of dielectric of uniform thickness \(t\) and relative permittivity \(\varepsilon_{1}\) is inserted between the plates. Find the change in electric energy of the capacitor if the plates are (a) isolated and (b) maintained at their initial potential difference by a battery.

Short Answer

Expert verified
Question: Calculate the change in electric energy of a parallel plate capacitor (a) when the plates are isolated, and (b) when the plates are maintained at their initial potential difference by a battery, after inserting a dielectric with thickness 't' and dielectric constant '\(\varepsilon_{1}\)'.

Step by step solution

01

(a) Change in electric energy when plates are isolated

Step 1: Calculate the initial capacitance without the dielectric \(C_{0} = \varepsilon_{0} A / x\) Step 2: Calculate the capacitance with the dielectric for the isolated case \(C_{1} = \varepsilon_{1} A / (x - t)\) Step 3: Calculate the initial electric energy without the dielectric \(E_{0} = \frac{1}{2} C_{0} V^2\) Step 4: Calculate the final electric energy with the dielectric for the isolated case \(E_{1} = \frac{1}{2} C_{1} V^2\) Step 5: Calculate the change in electric energy for the isolated case \(\Delta E = E_{1} - E_{0}\)
02

(b) Change in electric energy when plates are maintained at initial potential difference

Step 1: Calculate the initial capacitance without the dielectric (same as before) \(C_{0} = \varepsilon_{0} A / x\) Step 2: Calculate the capacitance with the dielectric for the maintained potential difference case \(C_{2} = \varepsilon_{0} A / (x - \frac{t}{\varepsilon_{1}})\) Step 3: Calculate the initial electric energy without the dielectric (same as before) \(E_{0} = \frac{1}{2} C_{0} V^2\) Step 4: Calculate the final electric energy with the dielectric for the maintained potential difference case \(E_{2} = \frac{1}{2} C_{2} V^2\) Step 5: Calculate the change in electric energy for the maintained potential difference case \(\Delta E = E_{2} - E_{0}\)

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A long cylindrical capacitor has radii \(a\) and \(b(b>a)\) and the space between the cylinders is filled with a dielectric of relative permittivity \(\varepsilon_{t}\) and dielectric strength \(K\). What is the maximum energy which can be stored per unit leagth of the capacitor?

An LIH dielectric sphere has a uniform polarization \(P\). Find an expression for the surface density of polarization charge \(\sigma_{p}\) at any point on the surface. Show that the 'depolarizing' field produced at the centre of the sphere by \(\sigma_{p}\) is \(P / 3 \varepsilon_{0}\).

A \(100 \mathrm{pF}\) parallel plate capacitor is charged to a potential difference of \(50 \mathrm{~V}\). The space between the plates is then completely filled with an insulating liquid of \(q_{1}=3\), a \(50 \mathrm{~V}\) battery being permanently connected across the plates. Find the new charge. If the filling had been carried out with the plates isolated from the battery, what would the new charge and potential difierence be?

Show that a surface density of charge given by \(\varepsilon_{0}\left(\varepsilon_{1}-1\right) E_{m}\) is alone sufficient to account for the appearance of \(\varepsilon_{\text {, }}\) in the denominators of Eqs \((11.3)\). \(E_{\mathrm{m}}\) is the E-field in the medium.

A rectangular box has two opposite faces of conducting material so that it forms a parallel plate capacitor. If it is one-third filled with an insulating liquid of \(\varepsilon_{t}=4\), find the ratio of the capacitance when the conducting faces are horizontal to that when they are vertical. (Neglect edge effects,)
See all solutions

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Famous Physicists

Read Explanation

Astrophysics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Scientific Method Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free