# Consider two metal spheres of radii

• Sunshine748
In summary, the formula for calculating the volume of a sphere is V = (4/3)πr³, the electric field between two metal spheres is inversely proportional to the distance between them and directly proportional to their radii, it can be zero if the spheres have equal radii and are at a specific distance known as the equilibrium distance, the charge on the spheres does not affect the electric field, and considering two metal spheres allows for the study of how the electric field changes with varying distances and sizes, with practical applications in fields such as electronics and engineering.
Sunshine748

## Homework Statement

Consider two metal spheres of radii r1 = R and r2 = 2R, both charged to the same potential V0.
a) What is the ratio n1/n2 of their surface charge densities?

## Homework Equations

n(eta) = charge/area
Er = -dV/dr

## The Attempt at a Solution

a) n1/n2 = Q/(4*pi*R2) / Q/(16*pi*R2) = 4

The answer is supposed to be 2, and I don't know what I'm doing wrong.

Last edited:
The spheres are charged to the same potential (volts), not the same charge (Coulombs).

## 1. What is the formula for calculating the volume of a sphere?

The formula for calculating the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere.

## 2. How is the electric field between two metal spheres related to their radii?

The electric field between two metal spheres is inversely proportional to the distance between the spheres and directly proportional to the radii of the spheres. This means that as the radii of the spheres increase, the electric field between them decreases.

## 3. Can the electric field between two metal spheres be zero?

Yes, the electric field between two metal spheres can be zero if the radii of the spheres are equal and they are placed at a specific distance from each other, known as the equilibrium distance. In this case, the electric forces between the spheres cancel each other out, resulting in a net electric field of zero.

## 4. How does the charge on the metal spheres affect the electric field between them?

The charge on the metal spheres does not affect the electric field between them. The electric field is solely determined by the distance between the spheres and their radii.

## 5. What is the significance of considering two metal spheres in this scenario?

Considering two metal spheres with different radii allows for the study of how the electric field changes with varying distances and sizes of the spheres. This can help in understanding the behavior of electric fields in more complex systems and can also have practical applications in fields such as electronics and engineering.

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