Final answer:
The intensity of current flowing through the conductor can be found using the magnetic field formula for a circular loop, and the time the loop remains in operation can be determined using the principle of conservation of charge.
Step-by-step explanation:
Calculating Current Intensity and Operation Time
To calculate the intensity of current flowing through the conductor (current intensity), we can use the formula for the magnetic field at the center of a single circular loop of current, which is given by B = (µ0 * I) / (2 * R), where µ0 is the permeability of free space, I is the current, and R is the radius. In this scenario, we're dealing with a loop of radius 2 cm and a magnetic field of 2µT at the center.
The formula can be rearranged to solve for current (I) as follows: I = (B * 2 * R) / µ0. Here, µ0 is approximately 4π * 10-7 T*m/A. We will need to convert the radius from centimeters to meters to use this equation.
Once we compute the current, regarding part b) of the question, to find out the time the loop remains in operation we can use the principle of the conservation of charge, which states that the total number of charges passing through a point in a time interval equals the current times the time. Therefore, time can be calculated by dividing the total charge by the current.
Since the number of electrons is given, we can calculate the total charge using the charge of a single electron, which is approximately 1.602 x 10-19 C. The total charge is the product of the number of electrons and the charge of a single electron. The time is then the total charge divided by the current found in part a).