Final answer:
The electric potential at the center of the Earth is zero if the potential at the surface is assigned a zero value, due to the properties of a uniformly charged sphere.
Step-by-step explanation:
The electric potential at the center of the Earth can be calculated using concepts from electrostatics and assuming Earth is a uniformly charged sphere. The potential due to a uniformly charged sphere is uniform inside the sphere and acts as if all the mass were concentrated at the center. Since the potential on the surface is defined as zero, the potential at the center is also zero. This is because the electrical potential is relative, and inside a conducting sphere, the potential is constant throughout.
To find the potential at the center of the Earth, we can use the equation for the potential due to a point charge: V = k * q / r, where V is the potential, k is the Coulomb constant, q is the charge, and r is the distance from the charge.
Since the potential at the surface of the Earth is assigned zero value, we can assume that the center of the Earth is located at a distance equal to the radius of the Earth, R. Therefore, the distance from the charge to the center of the Earth is also R.
Substituting the values into the equation, we get V = k * q / R.