Final answer:
Using the formula for the electric potential of a sphere, the potential near the surface of a Van de Graaff generator with a 1.95 m diameter sphere and a charge of 5.25 mC is approximately 45.77 MV.
Step-by-step explanation:
To calculate the potential near the surface of a metal sphere in a Van de Graaff generator, we can use the formula for the electric potential of a sphere,
V = k * Q / r,
where V is the electric potential, k is Coulomb's constant (8.99 x 109 N m2/C2), Q is the charge, and r is the radius of the sphere. Given that the diameter of the sphere is 1.95 m, the radius would be half of that, which is 0.975 m. Using the provided charge of 5.25 mC (which is 5.25 x 10-3 C), we can compute the potential V:
V = (8.99 x 109 x 5.25 x 10-3) / 0.975 ≈ 45.77 x 106 V
Therefore, the potential near the surface of the sphere is approximately 45.77 MV.