Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 12.5 cm, and the outer sphere has radius 14.8 cm. A potential difference of 120 V is applied to the capacitor. (a) What is the energy density at r = 12.6 cm, just outside the inner sphere? (b) What is the energy density at r = 14.7 cm, just inside the outer sphere? (c) For a parallel-plate capacitor the energy density is uniform in the region between the plates, except near the edges of the plates. Is this also true for a spherical capacitor?

Short Answer

Expert verified

(a)The energy density atr=12.6 just outside the inner sphere is:1.63×10-4J.m-3

(b) The energy density atr=12.6 just outside the inner sphere is8.8×10-5J.m-3

(c) No, the energy density is not uniformly distributed in the region between the plates except the near the edges of the plate.

Step by step solution

01

Calculating the density

Given,

rb=14.8cmra=12.5cmV=120V

Now, to get density we need to find the charge for hollow spheres, and the potential difference between the surface is given by:

Vab=kQ1ra-1rb

Substituting the values, we get:

Q=Vabk1ra-1rb=1209×10910.125-10.148=10.72×10-9C

Now, the density is given by:

u=Q232π2ε0r4

Substituting the values, we get:

u=10.72×10-9232π2×8.85×10-12×0.1264=1.63×10-4J.m-3

Therefore, the density is1.63×10-4J.m-3

02

Energy distribution

We, know that density is given by:

u=10.27×10-9232π2×8.85×10-12×0.1474=8.8×10-5J.m-3

Therefore, we can conclude that the energy density is not uniformly distributed, but decreases while being close to the outer shell.

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.

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

Small aircraft often have 24 V electrical systems rather than the 12 V systems in automobiles, even though the electrical power requirements are roughly the same in both applications. The explanation given by aircraft designers is that a 24 V system weighs less than a 12 V system because thinner wires can be used. Explain why this is so.

A beam of protons traveling at 1.20 km/s enters a uniform magnetic field, traveling perpendicular to the field. The beam exits the magnetic field, leaving the field in a direction pependicurlar to its original direction (Fig. E27.24). The beam travels a distance of 1.10 cm while in the field. What is the magnitude of the magnetic field?

Question: A high voltage dc power line falls on a car, so the entire metal body of the car is at a potential of with respect to the ground. What happens to the occupants (a) when they are sitting in the car and (b) when they step out of the car? Explain your reasoning.

A 1.50-mcylindrical rod of diameter 0.500cmis connected to

a power supply that maintains a constant potential difference of 15.0Vacross

its ends, while an ammeter measures the current through it. You observe that

at room temperature (20.0C)the ammeter reads 18.5Awhile at 92.0Cit

reads 17.2A. You can ignore any thermal expansion of the rod. Find (a) the

resistivity at and (b) the temperature coefficient of resistivity at for the material of the rod.

In the circuit shown in Fig. E26.47 each capacitor initially has a charge of magnitude 3.50 nC on its plates. After the switch S is closed, what will be the current in the circuit at the instant that the capacitors have lost 80.0% of their initial stored energy?

See all solutions

Recommended explanations on Physics Textbooks

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