Final answer:
OPTION A.The greatest charge that a particle can have, while moving at 30.0 m/s in a magnetic field of 0.500 x 10^-4 T without exceeding a force of 1.00 x 10^-12 N, is 6.67 x 10^-10 C.
Step-by-step explanation:
The question asks for the greatest charge a moving particle can have while being subjected to a force of less than 1.00 × 10-12 N in Earth's magnetic field, moving at a maximum speed of 30.0 m/s. The formula to calculate the magnetic force (F) on a moving charge (q) in a magnetic field (B) is F = qvBsin(θ), where v is the velocity of the charge and θ is the angle between the velocity of the charge and the magnetic field. Assuming the angle θ is 90 degrees to obtain the maximum force, and rearranging the formula to solve for charge, q = F / (vB), we can substitute the known values: F = 1.00 × 10-12 N, v = 30.0 m/s, and B = 0.500 × 10-4 T.
Therefore, the greatest charge q = (1.00 × 10-12 N) / (30.0 m/s × 0.500 × 10-4 T) = 6.67 × 10-10 C. This means that option a. 6.67 × 10-10 C is the correct answer. Comparing this charge with typical static electricity, we can conclude that it should not be too difficult to maintain a charge less than this on the equipment, given that common static charges are often greater and yet can be managed or prevented in sensitive measurements.