How can the electric potential of a dust grain in Saturn's rings be determined?

AI Thread Summary
To determine the electric potential of a dust grain in Saturn's rings, one must calculate the number of electrons needed to achieve a surface potential of -400V. The relevant equations include V = U/q and V = -W/q, where V is the electric potential, U is the potential energy, and q is the charge. The challenge lies in finding U, as the problem does not provide direct information on it. The discussion highlights the need for understanding the relationship between electric potential and charge, particularly for a spherical conductor. Ultimately, solving this problem requires applying fundamental concepts of electric potential and charge distribution.
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Homework Statement


Much of the material making up Saturn's rings is in the form of tiny dust grains having radii on the order of 10^-6 these grains are located in a region containing a dilute ionized gas, and they pick up excess electrons. As an approximation suppose each grain is sphereical, with radius R=1.0*10^-6m. How many electrons would one grain have to pick up to have a potential of -400V on its surface. (taking V=0 at infinity)?


Homework Equations


V=U/q
V=-W/q


The Attempt at a Solution


not quite sure where to start. I think V=-400=U/q but I don't know how to get U. I'd like to understand why U is relevant in this question also. Thanks
 
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What is the electric potential of a conducting sphere of radius r and charge Q ?
 
SammyS said:
What is the electric potential of a conducting sphere of radius r and charge Q ?

oh alright. is there another way to solve that problem without relying on that though. That equation is presented in a later section and the question is presented with only knowledge of potential energy and electric potential assumed.
 
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