Potential at the Center of a Uniformly Charged Hollow Sphere:

The potential at the center of a uniformly charged hollow sphere of radius R can be calculated using the formula for the electric potential due to a hollow sphere. The potential at any point inside the sphere is given by:

V = k * (Q / R)

where V is the potential, Q is the total charge on the sphere, R is the radius of the sphere, and k is the electrostatic constant.

Electric Field at a Distance r from the Center:

To find the electric field at a distance r from the center of the sphere, we can utilize Gauss's law. According to Gauss's law, the electric field inside a hollow sphere is zero.

This means that for r < r,="" the="" electric="" field="" is="" zero.="" however,="" for="" r="" /> R, we need to consider the electric field outside the sphere.

Calculating Electric Field for r > R:

The electric field outside the sphere can be determined by using the formula for the electric field due to a point charge. We can consider the entire sphere to be a point charge located at its center.

The formula for the electric field due to a point charge is given by:

E = k * (Q / r^2)

where E is the electric field, Q is the total charge on the sphere, r is the distance from the charge, and k is the electrostatic constant.

Since the entire charge of the sphere is concentrated at its center, the total charge Q is equal to the charge of the sphere.

Electric Field Calculation:

Therefore, the electric field at a distance r from the center of the sphere (r > R) is given by:

E = k * (Q / r^2)

where Q is the charge of the sphere.

Summary:

To summarize, the potential at the center of a uniformly charged hollow sphere of radius R is given by V = k * (Q / R). The electric field at a distance r from the center of the sphere (r > R) is given by E = k * (Q / r^2), where Q is the total charge on the sphere. Inside the sphere (r < r),="" the="" electric="" field="" is="" zero="" according="" to="" gauss's="" law.="" r),="" the="" electric="" field="" is="" zero="" according="" to="" gauss's="" />

V(r > R) = V(R/r)