Two conducting spheres connected by a wire

[gralla55]

Homework Statement

Two conduction spheres with radius R1 og R2 are connected with a conducting wire. The length difference between the spheres is large enough to neglect any effect their respective electric fields have on each other. The total charge of the system is Q.

Find the charges Q1 and Q2 on each of the spheres, expressed by R1, R2 and Q.

Find the size of the eletric field just outside each of the spheres. Show that the ratio between the sizes of the fields is reversed propotional to their respective radius.

The Attempt at a Solution

So what I did was to set their potentials equal to each other, and solve for Q1 and Q2 (see attachment). Nothing new here, but what confuses me is that they want me also to express Q1 and Q2 in terms of Q. I don't get why you would need Q (the total charge) to begin with when you have either Q1 or Q2...

The second part I did correct I believe.

Thanks for any input as usual!

 

[TSny]

You haven't actually found expressions for Q1 and Q2 separately. You found a relation between them which allowed you to answer the second part. The question assumes that R1, R2, and total charge Q are the "given" quantities. You are asked to find expressions for Q1 and Q2 in terms of the given quantities.

 

[gralla55]

Allright, but can't I just use the fact that Q2 = (Q - Q1), and substitute it into my equations like this? (attachment)

Thanks again!

 

[TSny]

Yes. Good. I think that's what they wanted.

 

[Nickie]

I would respond by saying that the total charge Q is necessary to determine the individual charges Q1 and Q2 on each sphere, as they are connected by a conducting wire and therefore share the same charge. The ratio between the sizes of the electric fields just outside each sphere is reversed proportional to their respective radius because the electric field strength is directly proportional to the charge and inversely proportional to the square of the distance. This means that as the radius increases, the distance from the center of the sphere to the outside also increases, resulting in a weaker electric field. Therefore, the larger sphere with a larger radius will have a smaller electric field compared to the smaller sphere with a smaller radius. This relationship is reflected in the equations for the electric field just outside each sphere, where the ratio of the electric fields is equal to the ratio of the radii.