- #1

- 104

- 0

## Homework Statement

An insulated spherical conductor of radius R1 carries a charge Q. A second conducting sphere of radius R2 and initially uncharged is then connected to the first by a long conducting wire.

(a) After the connection, what can you say about the electric potential of each sphere?

(b) How much charge is transferred to the second sphere?

(c) The spheres are assumed to be far apart compared to their radii. Why make this assumption?

## Homework Equations

## The Attempt at a Solution

(a) Once the spheres are "hooked up," they behave as one conductor. Because a conductor is an equipotential, the potential of each sphere is the same.

(b) Because the potentials have to be the same, the charge on each sphere is in

proportion to their radii:

[tex]

V = \frac{Q-\Delta Q}{R_1} = \frac{\Delta Q}{R_2}

[/tex]

Delta Q is the amount of charge exchanged between the spheres, and the total charge

should be Q because of conservation of charge. The final charges are then

[tex]

Q_1 = Q \frac{R_1}{R_1+R_2} \quad Q_2 = Q \frac{R_2}{R_1+R_2}

[/tex]

(c) No idea here. As the second sphere gains charge, shouldn't there be repulsion between the two (proportional to the inverse square of the separation distance)? But then what happens? I can't understand why the distance would matter.