Conducting sphere surrounded by insulator with dielectric constant

In summary: And, D = ε0 E in the dielectric material.Inside the conducting sphere, E = D = 0.In summary, the values of D, E, P, and ρ as a function of r for a conducting sphere surrounded by a dielectric material with varying dielectric constant can be determined by using Gauss's Law and the given equations. Outside the conducting sphere, D and E are related to q and r, while inside the sphere, D and E are both equal to zero.
  • #1
zhillyz
67
0

Homework Statement



A conducting sphere of radius A has a charge +Q on it and is surrounded by an insulating material whose dielectric constant varies with radius according to εr = 2exp[-(r/a-1)]2. The dielectric has a spherical outer boundary B. Find the values of D, E, P, ρ as a function of r.

Homework Equations



εr = 2exp[-(r/a-1)]2,

Gauss's Law?

The Attempt at a Solution



Outside conducting sphere:

D directed radially outward so using symmetrical surface integral form of Gauss law, D = q/4∏r2.

E=D/ε0 = q/4∏ε0r2.

Inside sphere:
D=0, E=0.

Not sure if this is right or what next steps to take?
 
Physics news on Phys.org
  • #2
zhillyz said:

Homework Statement



A conducting sphere of radius A has a charge +Q on it and is surrounded by an insulating material whose dielectric constant varies with radius according to εr = 2exp[-(r/a-1)]2. The dielectric has a spherical outer boundary B. Find the values of D, E, P, ρ as a function of r.

Homework Equations



εr = 2exp[-(r/a-1)]2,

Gauss's Law?

The Attempt at a Solution



Outside conducting sphere:

D directed radially outward so using symmetrical surface integral form of Gauss law, D = q/4∏r2.

E=D/ε0 = q/4∏ε0r2.

Inside sphere:
D=0, E=0.

Not sure if this is right or what next steps to take?
Hello zhillyz. Welcome to PF!

I take it that the spherical shell has inner radius A, and outer radius, B.

E = D/ε0 outside the dielectric shell; where r > B .

For A < r < B, E = D/εr .
 

1. What is a conducting sphere surrounded by an insulator with dielectric constant?

A conducting sphere surrounded by an insulator with dielectric constant refers to a setup in which a charged sphere made of a conducting material is placed inside an insulating material with a specific dielectric constant. This arrangement is commonly used in experiments to study the behavior of electric fields and charges.

2. How does the dielectric constant affect the electric field around the conducting sphere?

The dielectric constant of the insulating material surrounding the conducting sphere determines the strength of the electric field around the sphere. A higher dielectric constant means a stronger electric field, while a lower dielectric constant results in a weaker electric field.

3. What happens to the charge on the conducting sphere when it is surrounded by an insulator with dielectric constant?

When a conducting sphere is placed inside an insulating material with a dielectric constant, the charge on the sphere is redistributed. This is because the electric field strength is affected by the dielectric constant, causing the charges on the sphere to move and create a new equilibrium.

4. How does the distance between the conducting sphere and the insulator affect the electric field?

The distance between the conducting sphere and the insulating material directly affects the strength of the electric field. As the distance increases, the electric field strength decreases, and vice versa.

5. What are some real-life applications of a conducting sphere surrounded by an insulator with dielectric constant?

This setup is commonly used in experiments and demonstrations to study the behavior of electric fields. It is also used in electronic devices such as capacitors, which use a conducting sphere surrounded by an insulator (dielectric) to store electric charge. This setup is also used in high voltage equipment to reduce the strength of the electric field and prevent electrical breakdown.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
17
Views
327
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
5K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
309
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
8K
  • Introductory Physics Homework Help
3
Replies
78
Views
4K
Back
Top