Finding the charges on surfaces (hollow spheres)

[rela]

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

 

[pam]

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.

 

[Moetasim]

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,