Electric Potential And Potential Difference

When two hollow conducting spheres of radii and (where ) are given equal charges, we need to determine the electric potential on each sphere. The formula for the electric potential on the surface of a charged conducting sphere is given by:

where:

• is the electric potential.
• is Coulomb's constant.
• is the charge.
• is the radius of the sphere.

Since both spheres have the same charge , the potential on sphere 1 with radius , and the potential on sphere 2 with radius , are given by:

Given that , it follows that:

will be significantly smaller than

Therefore, the potential is more on the smaller sphere.

Answer: More on smaller sphere.

To determine the potential difference between two points and on a charged thin spherical shell, we need to consider the properties of potential inside and outside the shell. For a thin spherical shell:

• Inside the shell (any point within the radius of the shell), the electric potential is constant. This is because the electric field inside the shell is zero due to the symmetry and Gauss's law. Therefore, the potential difference between any two points inside the shell is zero.
• Outside the shell, the shell behaves as a point charge located at its center. The potential at a distance from the center is given by , where is the total charge on the shell, and .
• If the points and are both either inside or at the same radius from the center of the shell, the potential difference between them is zero.

Given that both points are either inside the shell or at the same radial distance, the potential difference is: Zero