Dielectrics and Maximum Potential Difference

[scdvm787]

Homework Statement

The radiation detector known as a Geiger Counter uses a closed hollow cylindrical tube with an insulated wire along its axis. Suppose a Geiger tube as its called has a 1.0mm diameter wire in a tube with a 25mm inner diameter. The tube is filled with a low pressure gas whose dielectric strength is 1.0*10^6 V/m. What is the maximum potential difference between the wire and tube?

Homework Equations

(delta)Vc=Ed

The Attempt at a Solution

I understand that the dielectric strength is the material's maximum sustainable electric field. I feel like you could set (delta)V = to Emax (dielectric strength) times the distance between the wire and the edge of the tube (.0125-.0005) and solve. However that seems too easy and doesn't seem totally right to me. That being said I really don't know how to start this problem. If someone could give me a push in the right direction and help me work it through I'd really appreciate it. Thanks in advance!

 

[anathema]

You are on the right track with your understanding of the dielectric strength and its relation to the maximum potential difference. However, your approach of using the distance between the wire and the edge of the tube may not be accurate. Instead, you should consider the distance between the wire and the inner wall of the tube, as this is where the electric field will be strongest.

To solve this problem, you can use the equation you mentioned, (delta)Vc=Ed, where (delta)Vc is the maximum potential difference, E is the electric field, and d is the distance between the wire and the inner wall of the tube. You can rearrange this equation to solve for (delta)Vc by dividing both sides by E. Then, you can substitute the given values for E (dielectric strength) and d (distance between wire and inner wall) to find the maximum potential difference.

I hope this helps guide you in the right direction. If you need further assistance, please don't hesitate to ask. Good luck with your problem-solving!

 

[Moetasim]

As a scientist, it is important to approach problems with a thorough understanding of the principles involved. In this case, the key concept is the relationship between electric field and potential difference (or voltage).

The equation (delta)V = Ed represents the change in potential (voltage) between two points in an electric field, where E is the strength of the electric field and d is the distance between the points. This equation assumes a uniform electric field, which may not be the case in this scenario.

To accurately determine the maximum potential difference between the wire and tube, we need to consider the geometry of the system. The wire and tube form a capacitor, with the wire as the positive plate and the tube as the negative plate. The distance between the plates is the thickness of the gas layer, which can be approximated as the difference between the inner diameter of the tube (25mm) and the diameter of the wire (1.0mm), or 0.024m.

The maximum potential difference that can be sustained by the gas is given by the equation Vmax = Ed, where E is the dielectric strength of the gas. Plugging in the given value for the dielectric strength (1.0*10^6 V/m) and the distance between the plates (0.024m), we get a maximum potential difference of 24,000 volts.

It is important to note that this is an idealized calculation and may not accurately represent the actual maximum potential difference that can be achieved in this system. Factors such as non-uniform electric fields and breakdown voltage of the gas may affect the actual value. It is always important to consider the limitations and assumptions made in any calculation.