Consider a spherical Gaussian surface of radius \(r\) with a particle that carries a charge \(+q\) at its center.

(a) On the Gaussian surface, what is the magnitude of the electric field due to the particle? 

(b) What is the electric flux through the sphere due to the charged particle?

(c) Combining your answers to parts \(a\) and \(b\), what is the relationship between the electric flux through the sphere and the enclosed charge \(q_{\text {enc }}\) ?

(d) Would this relationship change if you doubled the radius \(r\) of the sphere?