To determine the electric field generated by a charged sphere, we can utilize both Coulomb’s Law and Gauss’s Law.

Coulomb’s Law states that the electric field $E$ at a point due to a point charge $Q$ is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance $r$ from the charge to the point of interest. For a charged sphere, we can conceptualize it as being composed of an infinite number of infinitesimal point charges. By applying Coulomb’s Law to each of these point charges, we can calculate the electric field produced by them individually. To find the total electric field produced by the entire sphere, we then integrate the contributions from all these point charges.

Alternatively, we can apply Gauss’s Law, which provides another effective method for calculating the electric field due to a charged sphere. Gauss’s Law states that the electric flux $\Phi_E$ through a closed surface is proportional to the total charge $Q_{\text{enc}}$ enclosed within that surface. By selecting a spherical Gaussian surface that encompasses the charged sphere, we can exploit Gauss’s Law to find the electric field at any point outside the sphere.

Both methods will yield the same result for the electric field surrounding a charged sphere. The expression for the electric field $E$ due to a uniformly charged sphere is given by the formula:

In this equation, $E$ represents the electric field, $k$ is Coulomb’s constant, $Q$ denotes the total charge of the sphere, and $r$ is the distance from the center of the sphere to the point where the electric field is being evaluated.