Conducting Sphere and Shell.

In summary, a problem involving a solid conducting sphere of radius 20cm placed inside a spherical shell with inner radius 30cm and outer radius 40cm, with charges of 20uC and -10uC placed on the inner and outer conductors, respectively, in a medium with a dielectric constant of 5 is presented. The task is to find the electric flux density (D), electric field (E), and dipole moment per unit volume (P) at all points in space, as well as the total energy in the system. The calculations for each region of space are described, and it is questioned whether the inner charge contributes energy to the system.
  • #1
DR33
25
0
Here's the problem that I have been trying to solve:

A solid conducting sphere of radius 20cm is concentrically placed inside a spherical shell of inner radius 30 cm and outer radius 40cm. A Charge of 20uC is placed on the inner sphere, and a charge of -10uC is placed on the outer conductor. The dielectric constant of the medium between the 2 conductors is 5. Finc:
a) D, E and P at all points in space (all vectors)
b) the total energy in the system

Can anyone help me resolve this . Thakn you.
 
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  • #2
What do you mean by D, E and P?
E = Electric field?
D, P = ?
Thanks
 
  • #3
D = Electric Flux Density
P = Dipole Moment per unit Volume
 
  • #4
..

Anyone?
 
  • #5
[tex]R_1 = 0.2m, R_2 = 0.3m, R_3 = 0.4m[/tex]
For [tex]r < R_1[/tex],
Since the solid sphere is a conductor, the E field will be 0.
For [tex]R_1 < r < R_2[/tex],
[tex]\phi = \frac{q_{in}}{\varepsilon}[/tex]
[tex]\phi = E\times 4\Pi r^2[/tex]
So [tex]E = ...[/tex]
For [tex]R_2 < r < R_3[/tex],
It's same with first one.
For [tex]r > R_3[/tex],
Use the method as for [tex]R_1 < r < R_2[/tex] with [tex]q_{in}[/tex] being changed to [tex]-10\mu C[/tex] (I don't know if the inner most charge has to be taken into account because it's bounded by the spherical conductor, correct me if I'm wrong)
As for the energy, would the inner charge contribute energy to the system?
 

1. What is a conducting sphere?

A conducting sphere is a spherical object made of a material that allows for the free movement of electrons, such as metal. This allows for the sphere to have a net charge and to conduct electricity.

2. How does a conducting sphere differ from a non-conducting sphere?

A conducting sphere allows for the movement of electrons, while a non-conducting sphere does not. This means that a conducting sphere can have a net charge, while a non-conducting sphere cannot.

3. What is the difference between a conducting sphere and a conducting shell?

A conducting sphere is a solid object, while a conducting shell is a hollow object. Both are made of a conducting material, but a conducting shell has an empty space inside while a conducting sphere does not.

4. How does the electric field inside a conducting sphere or shell differ from the electric field outside?

Inside a conducting sphere or shell, the electric field is zero. This is because the free electrons in the material will automatically arrange themselves in such a way that the electric field cancels out. Outside the sphere or shell, the electric field behaves as if all of the charge of the sphere or shell is concentrated at its center.

5. What is the importance of conducting spheres and shells in physics and engineering?

Conducting spheres and shells are important in various applications, such as in electrical circuits, capacitors, and antennas. They also play a role in theoretical physics, particularly in understanding the behavior of electric fields and charges.

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