Final answer:
The total charge on a sphere with a uniformly distributed charge can be found from the electric potential at the sphere's center using the formula Q = Vr/k, where V is the potential, r is the radius of the sphere, and k is Coulomb's constant.
Step-by-step explanation:
When a charge is spread uniformly over the surface of a sphere with radius r and the electric potential at the sphere's center is V, we can determine the total charge on the sphere using the concept of electric potential due to a spherically symmetric charge distribution.
According to the principles of electrostatics, the potential at a distance r from the center of a charged sphere is the same as if all the charge were concentrated at a point at the center of the sphere. Therefore, the potential V at the surface of the sphere, which also holds at the center due to symmetry, can be given by the equation:
V = kQ/r
where k is Coulomb's constant, Q is the total charge on the sphere, and r is the radius of the sphere. Solving for Q gives us:
Q = Vr/k
Thus, the total charge Q on the sphere can be found using the given potential V and the radius r of the sphere.