A superconducting magnet carries a 100 A current through a 0.50-mm-diameter superconducting wire that is wound into a coil. How much charge flows through the wire in 15 minutes?

Verified step by step guidance

1. Understand the problem: The goal is to calculate the total charge that flows through the superconducting wire in 15 minutes. The relationship between current, charge, and time is given by the formula: $Q=It$, where $Q$ is the charge, $I$ is the current, and $t$ is the time.
2. Convert the time from minutes to seconds, as the SI unit of time in the formula is seconds. Use the conversion factor: $1\min =60s$. Multiply 15 minutes by 60 seconds per minute to get the time in seconds.
3. Substitute the given values into the formula. The current $I$ is 100 A, and the time $t$ is the value you calculated in the previous step. The formula becomes: $Q=100t$.
4. Perform the multiplication to calculate the total charge $Q$. Ensure that the units are consistent, with current in amperes and time in seconds, so the result will be in coulombs (C).
5. Interpret the result: The total charge $Q$ represents the amount of electric charge that flows through the wire in the given time period. This value is a measure of the total flow of electrons in the superconducting wire.

Key Concepts

Current

Current is the flow of electric charge in a circuit, measured in amperes (A). It represents the rate at which charge passes through a given point in the circuit. In this question, a current of 100 A indicates that 100 coulombs of charge flow through the wire every second.

Charge

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. Charge is measured in coulombs (C), and it can be positive or negative. The total charge that flows through the wire can be calculated by multiplying the current by the time duration.

Time

Time is a measure of the duration in which events occur, typically measured in seconds (s). In this context, the time duration of 15 minutes needs to be converted into seconds to calculate the total charge that flows through the wire. Since 1 minute equals 60 seconds, 15 minutes equals 900 seconds.