Finding the charges on surfaces (hollow spheres)

In summary, two hollow conducting spheres with a common center have dimensions as shown in the attached figure. The inner sphere has a charge of -200 nC while the outer sphere has a charge of +80 nC. The inner and outer surfaces are denoted by A, B, C, and D. The net charge on A+B+C must be zero and therefore the charge on C is +200 nC. The correct answer for the charge on D is -120 nC.
  • #1
rela
17
0
Dear all,

Two hollow conducting spheres have a common center O. The dimensions of the spheres
are as shown (attached above).

A charge of −200 nC is placed on the inner conductor and a charge of +80 nC is placed on the outer conductor. The inner and outer surfaces of the spheres are respectively denoted by A, B, C, and D, as shown. In the figure above, the charges on surfaces C and D respectively, in nC, are closest to:

I got it as +80 and -120

Not sure if it's correct too as I dun have the answers.

Hope you guys will help me out in the approach of solving this questions. Having some problems in visualizing.

Thanks again for the help.

Regards
Rela
 

Attachments

  • image.jpeg
    image.jpeg
    19.2 KB · Views: 668
Physics news on Phys.org
  • #2
The net charge on A+B+C must be zero so that E=0 in the conductor between C and D.
This means the charge on C must be +200.
Your answer for D is correct.
 
  • #3


Hello Rela,

Thank you for sharing your question with us. Finding the charges on the surfaces of hollow spheres can be a bit tricky, but I will try my best to explain the approach to solving this problem.

First, let's understand the concept of charge distribution on conducting surfaces. In a conductor, charges are free to move around and distribute themselves evenly on the surface. This is known as electrostatic equilibrium. Therefore, the charges on the outer surface of the inner sphere (surface C) and the inner surface of the outer sphere (surface D) will be distributed evenly.

Now, let's look at the charges given in the problem. A charge of -200 nC is placed on the inner conductor and a charge of +80 nC is placed on the outer conductor. Since the inner surface of the outer sphere (surface D) is closer to the -200 nC charge, it will have a higher negative charge compared to the outer surface of the inner sphere (surface C). This is because the negative charge on the inner conductor will repel the electrons on the outer surface of the inner sphere, causing them to move to the outer surface of the inner sphere.

To find the exact charges on surfaces C and D, we can use the concept of Gauss's Law. This law states that the electric flux through a closed surface is proportional to the enclosed charge. In this case, we can draw a Gaussian surface enclosing both spheres and use the given charges to calculate the electric flux. This will give us the values for the charges on surfaces C and D.

Using this approach, we can calculate the charges on surfaces C and D to be +80 nC and -120 nC, respectively. Therefore, your answer of +80 and -120 is correct. I hope this explanation helps you understand the approach to solving this problem. If you have any further questions, please let me know.

Best regards,
 

1. What is a hollow sphere and why is it important in finding charges on surfaces?

A hollow sphere is a spherical object with an empty space inside. It is important in finding charges on surfaces because it allows for a simplified calculation of the electric field and charge distribution on the surface.

2. How do you determine the charge on a hollow sphere?

The charge on a hollow sphere can be determined by using the Gauss's law. This law states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of the medium. By applying this law to a hollow sphere, the charge on the surface can be calculated.

3. Can a hollow sphere have a net charge of zero?

Yes, a hollow sphere can have a net charge of zero if the charges on the surface are distributed symmetrically. This means that the positive and negative charges cancel out, resulting in a net charge of zero.

4. What is the difference between a conducting and non-conducting hollow sphere in terms of charge distribution?

In a conducting hollow sphere, the charges on the surface will distribute themselves uniformly due to the repulsive forces between like charges. However, in a non-conducting hollow sphere, the charges will not redistribute themselves and will remain localized in the same areas where they were initially placed.

5. Can the charge on a hollow sphere change?

Yes, the charge on a hollow sphere can change if it is in contact with another charged object. This is because charges can transfer between objects through a process called conduction. Additionally, if an external electric field is applied, the charges on the surface may redistribute, resulting in a change in the net charge of the hollow sphere.

Similar threads

  • Introductory Physics Homework Help
Replies
17
Views
384
  • Introductory Physics Homework Help
Replies
11
Views
376
  • Introductory Physics Homework Help
Replies
18
Views
1K
  • Introductory Physics Homework Help
Replies
21
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
489
  • Introductory Physics Homework Help
Replies
21
Views
652
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
13
Views
1K
Back
Top