Find potential of a ball inside a grounded shell

In summary, the question is about finding the potential of a metal ball with initial potential v1 and surrounded by a conducting shell with radius r2, if the shell is grounded. The conversation discusses the relationship between the potential of the ball and the induced charge on the shell, and raises a question about whether the potential of the shell should be taken into account when finding the potential of the ball. The conclusion is that both approaches, accounting for the potential of the shell or assuming it is zero, are valid and result in similar outcomes.
  • #1
tigigi
38
0
I have this question that initially a metal ball of radius r1 with potential v1, then surrounded by a conducting shell with radius r2. Find potential of ball if shell grounded.

So v1 =kq/r1, then q=vr1/k, can I say directly that shell will have -q since it's induced by ball?
Then v ball will be kq /r1 + k(-q)/r2 ?
I'm not sure if I find should count the potential due to shell when I find the v ball?
Thanks for help.
 
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  • #2
Looks correct.
tigigi said:
I'm not sure if I find should count the potential due to shell when I find the v ball?
You'll need that, or the condition that the shell has a potential of zero. Both approaches are possible and looks very similar.
 

FAQ: Find potential of a ball inside a grounded shell

1. What is the purpose of finding the potential of a ball inside a grounded shell?

The purpose of finding the potential of a ball inside a grounded shell is to understand the electrostatic forces and interactions between the two objects. This can also help in predicting the behavior of the objects in an electric field.

2. How is the potential of a ball inside a grounded shell calculated?

The potential of a ball inside a grounded shell is calculated using the formula V = kQ/r, where V is the potential, k is the Coulomb's constant, Q is the charge of the ball, and r is the distance between the center of the ball and the center of the shell.

3. What is the effect of changing the distance between the ball and the shell on the potential?

The potential of a ball inside a grounded shell is inversely proportional to the distance between the two objects. This means that as the distance decreases, the potential increases and vice versa.

4. How does the charge of the ball affect the potential inside a grounded shell?

The charge of the ball has a direct effect on the potential inside a grounded shell. The larger the charge on the ball, the higher the potential will be inside the shell. This is because the electric field created by the charge will be stronger.

5. Can the potential inside a grounded shell ever be zero?

Yes, the potential inside a grounded shell can be zero. This occurs when the charge on the ball is equal and opposite to the charge on the shell. In this case, the electric fields from the two objects will cancel out, resulting in a net potential of zero.

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