Resistance between ball and bowl

In summary, the conversation discusses the calculation of resistance between a metallic ball and a semi-spherical bowl filled with salty water. The formula R = L/σA is mentioned, but it is determined to not be applicable in this scenario due to the variable A being unclear. Instead, it is suggested to use the current I, electric field E(r), and potential difference V to calculate the resistance.
  • #1
Piglet1024
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1. A metallic semi-spherical bowl is filled with salty water. A metallic ball is suspended at the center of the bowl, so that it is half submerged in the water. The outer radius of the ball is a, and the inner radius of the bowl is b. The conductivity of the water is [tex]\sigma[/tex]. Calculate the resistance between the ball and the bowl.



2. R=[tex]\frac{L}{\sigma A}[/tex]



3. So I thought that for A I could use the difference between the surface area of the bowl and the ball, but then I thought well what if I need to find the area of the cross sections because the original thought seemed too simplistic. L, I feel, is obviously (b-a) but I could be wrong. This is more of a conceptual question, but did I think of the correct method above or did I completely miss the point?
 
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  • #2


Your method won't work. That equation only applies to situations with a constant cross-sectional area, like a cylindrical wire. In this problem, you discovered that the meaning of A wasn't clear. When there's a question as to what the variables in an equation should equal, that's often a sign that you're not using the right equation.

What I would do is assume there's a current I flowing from the ball to the bowl. From that, you should be able to figure out the electric field E(r) and calculate the potential difference V between the ball and bowl. The resistance will then be V/I.
 

What is resistance between ball and bowl?

Resistance between ball and bowl is the force that opposes the motion of a ball rolling inside a bowl. It is caused by the friction between the surface of the ball and the surface of the bowl, as well as the air resistance.

How does the surface of the ball affect resistance between ball and bowl?

The type of surface on the ball can greatly affect the resistance between ball and bowl. A rough surface on the ball will result in more friction and therefore more resistance. A smooth surface will result in less friction and less resistance.

Does the size of the ball or bowl affect resistance between ball and bowl?

Yes, the size of the ball and bowl can affect the resistance between them. The larger the ball or bowl, the more surface area there is for friction to occur, resulting in more resistance. Similarly, a smaller ball or bowl will have less surface area and therefore less resistance.

Can the speed of the ball affect resistance between ball and bowl?

Yes, the speed of the ball can affect resistance between ball and bowl. The faster the ball is rolling, the more air resistance it will experience, which can increase the overall resistance between the ball and bowl.

How can resistance between ball and bowl be reduced?

Resistance between ball and bowl can be reduced by using a smoother surface on the ball, using a larger ball or bowl, and reducing the speed at which the ball is rolling. Additionally, using a lubricant on the surface of the ball or bowl can also reduce friction and resistance.

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