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# How Do You Find The Electric Potential At The Center Of A Sphere: Unveiling The Secret

How Do You Find The Electric Potential At The Center Of A Sphere: Unveiling The Secret

## Electric Potential Of A Conducting Sphere

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## What Is The Formula For The Electric Potential At The Centre Of A Sphere?

Certainly, let’s clarify and expand upon the information regarding the formula for electric potential at the center of a sphere:

The electric potential at the center of a charged conducting sphere can be calculated using the formula V = k * (Q / r), where:

• V represents the electric potential at the center of the sphere.
• k is Coulomb’s constant, which has a value of approximately 8.99 x 10^9 Nm²/C².
• Q is the total charge of the sphere, usually measured in coulombs (C).
• r stands for the radius of the sphere in meters (m).

This formula essentially states that the electric potential at the center of a charged sphere is equivalent to the potential created by a point charge with the same charge (Q) placed at the center of the sphere. It is important to note that this formula is applicable for conducting spheres, where the charge is uniformly distributed over the surface of the sphere. The electric potential at any point within the sphere is the same due to its spherical symmetry. This concept is a fundamental principle in electrostatics and plays a crucial role in understanding the behavior of electric fields and potentials in various situations involving charged spheres.

## What Is The Electric Potential At The Centre Of A Spherical Shell?

To determine the electric potential at the center of a spherical shell, you can use the formula: V = (1 / (4πε₀)) * Q, where ε₀ represents the electric constant (also known as the vacuum permittivity), and Q is the total charge enclosed within the shell.

Consider the scenario where a point charge q is positioned inside a conducting spherical shell with an inner radius of 2R and an outer radius of 3R. This point charge is situated at a distance of R from the center of the shell. To calculate the electric potential at the center of the shell, you need to find the total charge Q enclosed within the shell, and then apply the formula mentioned above.