Electric Potential of Two Spheres

In summary: The charge transferred to the second sphere is Q2 = Q1(r2/r1) (Why make this assumption?)In summary, after connecting an insulated spherical conductor of radius r1 with charge Q to a second uncharged conducting sphere of radius r2, the electric potential on each sphere is equal, given by kQ1/r1 = kQ2/r2. The amount of charge transferred to the second sphere is Q2 = Q1(r2/r1). This assumption is made because the connected spheres are far apart compared to their radii, resulting in a negligible change in the electric potential and charge distribution.
  • #1
boderam
24
0
Problem:

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. After the connection, what can you say about the electric potential of each sphere? How much charge is transferred to the second sphere? Assume the connected spheres are far apart compared to their radii. (Why make this assumption?)


I think I am confused about potential in general, so bare with me here. I know that for a point charge Q the potential at a point P is kQ/r. In class my teacher derived the potential for a sphere, in the case of the first sphere it would be kQ/r. The charge then distributes to the other sphere, but I am not sure how to derive the balance. I also know that the potential will be the same on both spheres since they are conducting, the electric field is 0. Let the first sphere have charge Q1 and the second Q2, then Q = Q1 + Q2. V = kQ1/r = kQ2/r since the potentials are equal...I don't think is right though. Someone want to clear this up for me? Thanks. A lot.
 
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  • #2
anyone know how to do this?
 
  • #3
Yeah that's right, the potential of each sphere is equal after they're connected, so kQ1/r1=kQ2/r2.
 

FAQ: Electric Potential of Two Spheres

What is the concept of electric potential of two spheres?

The electric potential of two spheres refers to the measure of the potential energy per unit charge at any point between two charged spheres. It is a measure of the potential difference between the two spheres, and can be positive, negative, or zero depending on the relative charges of the spheres.

How do you calculate the electric potential of two spheres?

The electric potential of two spheres can be calculated using the formula V = k(Q1/r1 + Q2/r2), where V is the electric potential, k is the Coulomb constant, Q1 and Q2 are the charges of the two spheres, and r1 and r2 are the distances from the center of each sphere to the point where the potential is being measured.

What is the relationship between electric potential and electric field of two spheres?

The electric potential and electric field of two spheres are closely related. The electric field is the gradient of the electric potential, meaning that it is the rate of change of the potential with respect to distance. As the potential decreases or increases, the electric field also decreases or increases, respectively.

How does the distance between the two spheres affect the electric potential?

The distance between the two spheres has a direct impact on the electric potential. As the distance increases, the potential decreases because the electric field weakens. This is due to the inverse square law, which states that the electric field strength decreases with the square of the distance from the source.

Can the electric potential of two spheres be negative?

Yes, the electric potential of two spheres can be negative. This occurs when the two spheres have opposite charges, as the potential at a point between them will be negative relative to the potential at infinity. It is important to remember that the sign of the potential is arbitrary and does not affect the physical behavior of the system.

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