# Force between two spheres connected by wire and battery

**1. The problem statement, all variables and given/known data**

There are two alike initially uncharged spheres of radius r at a distance of d>>r, as shown in the figure.

a) Switch ##K_2## is closed. What is the force exerted between the two spheres?

b) What would be the force between the two spheres, if in the previous experiment instead of closing switch ##K_2##, switch ##K_1## was closed?

c) Determine the force exerted between the spheres if both switches are closed.

**2. Relevant equations**

**3. The attempt at a solution**

In part a), if the battery sends a charge of ##Q## to the left sphere, then it must send a charge of -Q to the right sphere. Equating the potential difference gives:

$$\frac{2kQ}{R}=U \Rightarrow Q=\frac{UR}{2k}$$

Hence, the magnitude of force between the spheres is:

$$F=\frac{kQ^2}{d^2}=\frac{kU^2R^2}{4k^2d^2}$$

The force is attractive.

Is this correct?

In part b), I really have no idea. How do I deal with this case? :confused:

Any help is appreciated. Thanks!

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