Two identical metal spheres have charges of q1 and q2. They are brought together so they touch, and then they are separated. (a) How is the net charge on the two spheres before they touch related to the net charge after they touch? (b) After they touch and are separated, is the charge on each sphere the same? Why?

(a) Net charge, q1 + q2, stays the same.

(b) Since they are the same size and become equipotential by touching,
the final q1' and q2' are equal. Call that charge q

q1 + q2 = 2q
q1' = q2' = (q1 + q2)/2

2Q

I apologize, I don't understand your request. Can you please provide more context or information about what you're referring to?

To answer these questions, let's consider the process step by step.

(a) How is the net charge on the two spheres before they touch related to the net charge after they touch?

Before the spheres touch, the net charge on each sphere is represented by q1 and q2, respectively. The net charge on the two spheres before they touch can be determined by simply adding q1 and q2 together.

When the two spheres touch, they become conductive. This means that electrons are free to move between the spheres. Electrons will redistribute themselves to reach equilibrium.

The net charge after the spheres touch will depend on the relative magnitudes of q1 and q2. If q1 is greater than q2, electrons will flow from the sphere with greater charge (q1) to the one with lesser charge (q2). As a result, the sphere with initial charge q1 will lose some charge, and the sphere with initial charge q2 will gain some charge.

However, if q2 is greater than q1, the opposite will happen. Electrons will flow from the sphere with initial charge q2 to the one with initial charge q1, resulting in the redistribution of charges.

In either case, the net charge on the two spheres after they touch is the same as the sum of the initial charges (q1 + q2). The total charge remains conserved, but the distribution between the two spheres changes.

(b) After they touch and are separated, is the charge on each sphere the same? Why?

No, the charge on each sphere will not necessarily be the same after they touch and are separated. The distribution of charge between the spheres will depend on the initial charges (q1 and q2).

If q1 and q2 were equal initially, the charges will redistribute equally, resulting in the same charge on each sphere after they are separated.

However, if q1 and q2 were unequal initially, the charges will redistribute according to the relative magnitudes of the initial charges. The final charge on each sphere will depend on the exchange of electrons during the touching process.

In summary, the charge on each sphere after they touch and are separated will depend on the initial distribution of charges and the subsequent redistribution of electrons between the spheres.

+Q and -Q remains the same

Same size