# 2 point charges with sphere inbetween

• Cairrd
In summary, to solve the problem of two point charges q and -q placed 2d apart, a conducting sphere with a small radius r (where r << 2d) can be placed midway between the charges. This will increase the force on each charge by a factor of approximately (1 + 16 (r^3/d^3)) by using the method of images and treating the two images as a dipole when calculating the total force.
Cairrd
I am having a little trouble knowing how to approach the following question:

Twi point charges q and -q are placed 2d apart. Show that a conducting sphere of small radius r (where r << 2d) is placed midway between the charges, show the force on each is increased by a factor of approx (1 + 16 (r^3/a^3)).

Anyone want to help me here?

Thanks

Use the method of images on the conducting sphere, and then treat the two images as a dipole when you calculate the total force on one charge due to the other charge and the image charges.

Also, I assume you mean d, not a, in your factor.

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## 1. What is the concept of "2 point charges with sphere inbetween"?

The concept of "2 point charges with sphere inbetween" refers to a scenario in which two electric charges are placed on either side of a conducting sphere. This creates an electric field between the two charges that is affected by the presence of the conducting sphere.

## 2. How does the presence of the conducting sphere affect the electric field between the two point charges?

The conducting sphere acts as a shield, redistributing the electric field between the two point charges and reducing its strength. This phenomenon is known as electrostatic shielding.

## 3. What factors influence the strength of the electric field in this scenario?

The strength of the electric field between the two point charges is influenced by the magnitude of the charges, the distance between them, and the dielectric constant of the material surrounding them.

## 4. How is the direction of the electric field affected by the conducting sphere?

The conducting sphere affects the direction of the electric field by redirecting the field lines and causing them to curve around the surface of the sphere. Inside the conducting sphere, the electric field is zero.

## 5. What is the significance of the conducting sphere in this scenario?

The conducting sphere plays a critical role in reducing the strength of the electric field between the two point charges and redistributing it in a way that minimizes its effects on the surrounding environment. This phenomenon is important in various fields such as electronics, telecommunications, and electrostatics.

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