Final answer:
The magnitude of the earth's gravitational field midway between the center and the surface of the earth can be calculated using Newton's law of gravitation.
Step-by-step explanation:
The magnitude of the earth's gravitational field midway between the center and the surface of the earth can be calculated using Newton's law of gravitation. The gravitational field strength, g, at this point is given by the equation g = GM/r^2, where G is the gravitational constant, M is the mass of the earth, and r is the distance from the center of the earth.
Since we are assuming a uniform mass distribution, the mass of the earth can be approximated as the average density multiplied by the volume of the earth, which is given by M = (4/3)πr^3ρ, where ρ is the density of the earth.
Substituting the expression for M into the equation for g and simplifying, we can find the magnitude of the gravitational field midway between the center and the surface of the earth.