Final answer:
To determine the charge on a metal ball from the electric field strength at a point away from its surface, use the electric field formula for a point charge. By solving the equation with the given values, we find that the charge on the ball is 5.4 nC.
Step-by-step explanation:
To find the charge on the metal ball, we can use the formula for the electric field E created by a point charge at a distance r from its surface. This formula is E = k * Q / r^2, where k is Coulomb's constant (approximately 8.99 x 10^9 N*m^2/C^2), Q is the charge, and r is the distance from the charge. Since the metal ball can be treated as a point charge for points outside of it, we can use the given electric field strength to solve for Q. The distance r is 3.5 cm + 5 cm (half the diameter of the ball) to the center of the ball, which is 8.5 cm or 0.085 m.
Plugging in the numbers, we get:
60,000 N/C = (8.99 x 10^9 N*m^2/C^2) * Q / (0.085 m)^2
Solving for Q gives us:
Q = (60,000 N/C) * (0.085 m)^2 / (8.99 x 10^9 N*m^2/C^2)
Q = 5.4 x 10^-9 C
To convert this charge into nanocoulombs (nC), we multiply by 10^9 nC/C:
Q = 5.4 x 10^-9 C * 10^9 nC/C
Q = 5.4 nC
Therefore, the charge on the ball is 5.4 nC.