Two thin conducting spheres

• ambull
In summary, the problem involves two thin conducting spheres, one inside the other, with total charges of +Q and -Q and radii of R1 and R2 respectively. The magnitude of the charges is Q = 500 nC and the radii are R1 = 0.5 cm and R2 = 5.5 cm. The formula for calculating the energy required to move one electron from the outer sphere to the inner sphere is W=kQ(-e)(1/R1- 1/R2), which results in an energy of 130.9.
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

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.

What are "Two thin conducting spheres"?

"Two thin conducting spheres" refer to two spherical objects made of a material that allows electricity to flow through it easily. These spheres are often used in experiments and calculations related to electricity and magnetism.

What is the significance of studying two thin conducting spheres?

Studying two thin conducting spheres allows scientists to better understand the behavior of electricity and magnetism in a controlled setting. It also helps in developing and testing theories related to these phenomena.

What is the relationship between the distance between the two spheres and the electric field strength?

The electric field strength between two thin conducting spheres is inversely proportional to the distance between them. This means that as the distance between the spheres increases, the electric field strength decreases and vice versa.

How does the charge distribution on the spheres affect the electric field between them?

The charge distribution on the spheres affects the electric field between them. If the spheres have equal and opposite charges, the electric field between them will be stronger. If the spheres have the same charge, the electric field between them will be weaker.

Can two thin conducting spheres have the same charge?

Yes, two thin conducting spheres can have the same charge. However, this would result in a weaker electric field between them compared to if they had opposite charges. The strength of the electric field is determined by the magnitude and distribution of the charges on the spheres.

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