# Force on a sphere in a constant external electric field

• captain.joco
In summary, the question asks about the force on an uncharged solid sphere placed in a constant external electric field. The electric potential, electric field, and surface charge density have been determined, but the calculation of the force is uncertain. Suggestions and clarification have been given, and it has been determined that the force will depend on the presence of charge separation and the assumption that the electric field remains uniform.
captain.joco

## Homework Statement

An uncharged solid sphere is paced in a constant external electric field E0. What is the force on the sphere?

## The Attempt at a Solution

I know ( already have found ) the electric potential and electric field around the sphere. Also worked out the surface charged density. I don't know how to calculate the force..Any help please?

Isn't F = q*E ?

It seemed too simple somehow... Is q the induced charge on the sphere, and E the electric field close to the sphere??

captain.joco said:
It seemed too simple somehow... Is q the induced charge on the sphere, and E the electric field close to the sphere??

If there is charge separation, what will the net force be?

Got it! Thanks a lot for the help!

This is the exact question i was looking for help with and still not sure of what the next step is.

I know the uniform E-field causes the sphere to gain an induced dipole. From this how do you get the force? Is it ok to just assume the E-field remains uniform.. this can't be right as there would then be no force and seems there must be a force from the way the question is worded.

## 1. What is the force on a sphere in a constant external electric field?

The force on a sphere in a constant external electric field is a vector quantity that represents the strength and direction of the force exerted on the sphere by the electric field. It is given by the equation F = qE, where q is the charge of the sphere and E is the magnitude of the electric field.

## 2. How is the direction of the force determined on a sphere in a constant external electric field?

The direction of the force on a sphere in a constant external electric field is determined by the direction of the electric field and the charge of the sphere. If the charge and electric field are in the same direction, the force will be in the same direction. If they are in opposite directions, the force will be in the opposite direction.

## 3. How does the size of the charge affect the force on a sphere in a constant external electric field?

The size of the charge on the sphere directly affects the magnitude of the force. The larger the charge, the greater the force will be. However, the direction of the force will still depend on the direction of the electric field.

## 4. Is the force on a sphere in a constant external electric field affected by the size of the sphere?

Yes, the force on a sphere in a constant external electric field is affected by the size of the sphere. This is because the charge on the sphere is spread out over its surface, so a larger sphere will have a larger surface area and therefore a greater amount of charge. This results in a larger force being exerted on the larger sphere.

## 5. Can the force on a sphere in a constant external electric field be negative?

Yes, the force on a sphere in a constant external electric field can be negative. This occurs when the charge of the sphere is opposite in sign to the direction of the electric field. In this case, the force will be in the opposite direction of the electric field, resulting in a negative force value.

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