Respuesta :
The given question is incomplete. The complete question is as follows.
Two hollow conducting spheres (radius r) with a uniformly distributed charge are placed a distance d apart center to center. A thin wire with a switch S is connected to the surface of each sphere. The switch is initially open.
a. What is the potential between points a and b?
b. If the switch is then closed, what is the charge on each sphere at time [tex]t \rightarrow \infty[/tex].
c. What is the potential between points a and b after the sphere reaches its steady state?
Explanation:
(a) In order to bring a positive test charge from infinity to a point 'a', the work done is equal to the potential energy of the charge at point 'a'.
Hence, [tex]V_{a} = \frac{1}{4 \pi \epsilon_{o}} \frac{q}{a}[/tex]
Now, work done in bringing a positive test charge from infinity to point 'b' is equal to the potential energy of the charge at point 'b'.
[tex]V_{b} = \frac{1}{4 \pi \epsilon_{o}} \frac{-q}{b}[/tex]
[tex]V_{a} - V_{b} = \frac{q}{4 \pi \epsilon_{o}}(\frac{1}{a} + \frac{1}{b})[/tex]
Therefore, the potential between points a and b is as follows.
[tex]V_{a} - V_{b} = \frac{q}{4 \pi \epsilon_{o}}(\frac{1}{a} + \frac{1}{b})[/tex]
(b) As the spheres are connected through a conducting wire then charges will flow from one sphere to another unless and until the charge on both the sphere will become equal. In this case, it is equal to zero.
(c) Since, the charge of both the spheres is equal to zero so, no work is necessary to bring another charge to a and b. Therefore, potential difference between the points will also become equal to zero.
