Two thin conducting spheres

[ambull]

Homework Statement

two thin conducting spheres, one inside the other. They are both centered about the same point. The outer sphere has a total charge Q and radius R2 and the inner sphere has a total charge -Q and radius R1.

The magnitude of the charges is Q = 500 nC, and the radii are R1 = 0.5 cm and R2 = 5.5 cm.

How much energy would you need to expend to move one electron from the outer sphere to the inner sphere?

Homework Equations

W=kQ(-e)(1/R1- 1/R2)

The Attempt at a Solution

W=kQ(-e)(1/R1- 1/R2)= 130.9

 

[Shooting Star]

Your approach is correct.

 

[Moetasim]

x 10^-18 Joules

I would like to clarify the context of this problem. Are the spheres in a vacuum or in a medium with a specific dielectric constant? This information is important because it affects the value of the constant k in the equation. Assuming the spheres are in a vacuum, the value of k would be 8.99 x 10^9 Nm^2/C^2.

Based on the given information, we can calculate the energy required to move one electron from the outer sphere to the inner sphere using the equation W=kQ(-e)(1/R1- 1/R2). Substituting the values, we get W = (8.99 x 10^9 Nm^2/C^2)(500 x 10^-9 C)(-1.6 x 10^-19 C)(1/0.005 m - 1/0.055 m) = 130.9 x 10^-18 Joules.

This means that in order to move one electron from the outer sphere to the inner sphere, we would need to expend 130.9 x 10^-18 Joules of energy. This is a very small amount of energy, but it is necessary to overcome the attractive force between the opposite charges on the spheres.