To determine how many electrons cross a point in the wire with the given current function i(t) = 15 2 cos(2π 60t) [A] over the interval 0 < t < 0.001, one must first calculate the total charge that flows through the wire during that time. The relationship between current and charge is established by the equation: current = charge/time, allowing for integration of the current function over the specified time interval to find the total charge. Once the total charge is calculated, it can be converted to the number of electrons by dividing by the elementary charge (approximately 1.6 x 10^-19 coulombs). The discussion highlights confusion about the integration process and whether direct substitution of values would suffice. Understanding the integration approach is essential for accurately solving the problem.
