Is My Calculation of the Radius in a Dielectric Strength Problem Correct?

[kris24tf]

Dielectric Strength problem. Please Help! :(

If anyone can let me know if I went about this right, I'd appreciate it, as well as any advice.

The dielectric strength of an insulating material is the maximum electric field strength to which the material can be subjected without electrical breakdown occurring. Suppose a parallel plate capacitor is filled with a material whose dielectric constant is 3.5 and whose dielectric strength is 1.4 E 7 N/C. If this capacitor is to store 1.7 E -7 C of charge on each plate without suffering breakdown, what must be the radius of its circular plates?

I started with the equation E=Q/Eo*k*A, then found that A=Q/Eo*k*E.

I then plugged the numbers into this equation to get 2.3E-7/8.85E-12(3.5)(1.4E7).

Is this the right way to do this problem or do I need to do something differently, as I'm not sure if the radius they're looking for could be found with the Area I got?

 

[Nate810]

The answer should be 2.8E-4 m.To get the radius, you need to use A = πr2. So, rearrange the equation to solve for r and you will get:r = √(A/π)Plug in your value for A and you will get r = 2.8E-4 m.

 

[kyle8921]

Your approach to the problem is correct. The equation E=Q/Eo*k*A is the correct equation for calculating the electric field strength in a parallel plate capacitor. And finding the area using A=Q/Eo*k*E is also correct.

However, in order to find the radius of the circular plates, you will need to use the equation for the area of a circle, which is A=πr^2. This means that you will need to rearrange the equation to solve for the radius (r), which would be r=sqrt(A/π).

Once you have the value for the area, you can plug it back into the equation A=Q/Eo*k*E to find the radius. So your final equation would be r=sqrt((1.7E-7)/(8.85E-12*3.5*1.4E7*π)).

I would also recommend double checking your units to ensure they are consistent and to use scientific notation for easier calculations.

Additionally, it is always a good idea to double check your answer and do a quick sanity check to make sure it makes sense. In this case, the radius of the plates should be in meters, so if you get a value in a different unit, it may be a sign that you made a mistake in your calculations.

Overall, your approach and equations are correct, but just be sure to use the correct equation for finding the radius and to double check your units and answer.