Circulation of Magnetic Fields in Amperian Loops
Calculating Circulation in Amperian Loops
If the circulation of the magnetic fields is calculated around each Amperian loop, which of the following statements would be true?
Choose all that are correct. More than one statement may be true.
- The magnitude of the circulation will be greatest in loop B.
- The sign of the circulation will be positive for loop C.
- The magnitudes of the circulations will be the same for all three loops.
- The sign of the circulation will be positive for loop B.
- The sign of the circulation will be positive for loop A.
Analysis of Circulation in Amperian Loops
To determine the statements that are true, we need to analyze the given information.
Statement 1
The magnitude of the circulation will be greatest in loop B.
Statement 2
The sign of the circulation will be positive for loop C.
Statement 3
The magnitudes of the circulations will be the same for all three loops.
Statement 4
The sign of the circulation will be positive for loop B.
Statement 5
The sign of the circulation will be positive for loop A.
Let's evaluate each statement:
Statement 1
To determine the magnitude of the circulation, we need to consider the contribution of the magnetic field from each wire within the loop. In loop B, there are two current-carrying wires. The magnetic field due to the currents in both wires will contribute to the circulation.
However, in loops A and C, there is only one current-carrying wire inside each loop. Therefore, the statement is true. The magnitude of the circulation will be greatest in loop B.
Statement 2
The sign of the circulation depends on the direction of the current and the direction of the loop. In loop C, the current flows in a clockwise direction, as indicated by the thick arrow.
The arrowhead on the loop indicates the direction of circulation. Since the current and the loop have the same direction, the circulation will be positive. Therefore, the statement is true. The sign of the circulation will be positive for loop C.
Statement 3
Based on the analysis in statement 1, the magnitude of the circulation will be greatest in loop B. Therefore, the statement is false. The magnitudes of the circulations will not be the same for all three loops.
Statement 4
The direction of the circulation in loop B is indicated by the arrowhead on the loop. To determine the sign, we need to consider the direction of the current and the direction of the loop.
Since the current in the wire on the left is in the opposite direction to the loop, the circulation will be negative. Therefore, the statement is false. The sign of the circulation will not be positive for loop B.
Statement 5
Similar to statement 4, the direction of the circulation in loop A is determined by the current and the loop's direction. In this case, the current in the wire on the left is in the same direction as the loop.
Thus, the circulation will be positive. Therefore, the statement is true. The sign of the circulation will be positive for loop A.
In summary, the correct statements are:
- - The magnitude of the circulation will be greatest in loop B.
- - The sign of the circulation will be positive for loop C.
- - The sign of the circulation will be positive for loop A.