# Electric field strength and electric potential in a sphere

• Kurokari
In summary, the conversation discusses the concept of electric field strength and potential in a solid metal sphere. The charges are evenly distributed on the surface, resulting in zero electric field strength at the center due to the canceling out of opposite directions. The potential is also constant throughout the sphere, with the interior having the same potential as the surface. This is determined by the formula for the potential of a charged sphere.
Kurokari
Given a solid metal sphere where all the positive charges are distributed evenly on the surface of the metal sphere.

My textbook says that there is no electric field strength in the middle of the metal sphere because the charge = 0. However, my understanding is that wouldn't the center of the metal sphere be under the influence of the charges on the metal sphere surface, but because of the shape, all the electric field strength acts in opposite direction thus cancelling each other out.

The second question is, when there is no electric field strength, the electric potential is zero , that would mean that potential is either maximum or minimum given, E = - dV/dr . So why is it maximum in the sphere, why not minimum? What is that explanation?

Hi Kurokari,

1. You're right. Zero charge at a point doesn't mean zero filed at that point.

2. Zero field means a constant potential. The sphere has a constant potential. The same potential for the interior. I assume you are aware of the formula for the potential of a charged sphere.

## 1. What is the difference between electric field strength and electric potential?

Electric field strength measures the force that a charged particle experiences in an electric field, while electric potential measures the potential energy per unit charge at a specific point in the electric field.

## 2. How does electric field strength and electric potential vary in a sphere?

In a sphere, both electric field strength and electric potential vary with distance from the center of the sphere. As the distance from the center increases, the electric field strength and electric potential decrease.

## 3. What is the formula for calculating electric field strength in a sphere?

The formula for electric field strength in a sphere is E = kQ/r², where k is the Coulomb's constant, Q is the charge of the sphere, and r is the distance from the center of the sphere.

## 4. How is electric potential related to electric field strength in a sphere?

Electric potential is directly proportional to electric field strength in a sphere. This means that as the electric field strength increases, so does the electric potential.

## 5. Can electric field strength and electric potential be negative in a sphere?

Yes, electric field strength and electric potential can be negative in a sphere. A negative electric field strength indicates that the direction of the electric field is opposite to the direction of the positive charge, while a negative electric potential indicates that the electric potential energy is decreasing with distance from the center of the sphere.

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