Final answer:
Approximately 111 µC of charge is needed to raise an isolated metal sphere of radius 1.0 m to a potential of 1.0 × 10^6V using the formula Q = V * r / k where V is the potential, k is Coulomb's constant, and r is the radius.
Step-by-step explanation:
To determine how much electrical charge is required to raise an isolated metal sphere of radius 1.0 m to a potential of 1.0 × 10^6V, we can use the formula for the potential (V) of a charged sphere, which is V = k * Q / r, where V is the potential, k is Coulomb's constant (approximately 8.99 × 10^9 Nm^2/C^2), Q is the charge, and r is the radius of the sphere.
Assuming we want our sphere at a potential V = 1.0 × 10^6V and given that the radius r = 1.0 m, we can rearrange the formula to solve for Q (the charge):
Q = V * r / k
Q = (1.0 × 10^6V) * (1.0 m) / (8.99 × 10^9 Nm^2/C^2)
Q = 1.0 × 10^6 Vm / 8.99 × 10^9 Nm^2/C^2
Q = 1.11 × 10^-4 C
Therefore, approximately 111 µC (microcoulombs) of charge is needed to achieve a potential of 1.0 × 10^6V on an isolated metal sphere of radius 1.0 m.