Ampere's law EM 35 Ampere's law states that the line integral of the magnetic field around a closed loop (often called an Amperian loop) is directly proportional to the net current encircled by the loop: $ B . di = M lenc, Where u is a constant. The sign of the encircled current is defined to be positive if the current passes through the loop in the same direction as the area vector. E. If you have not done so already, use Ampere's law to determine the line integral around the loop in case 3 on the previous page, and write your answers in the table. F. In the last two columns of the table on the previous page, indicate the value and sign of the encircled current through each loop, for each direction of the area vector. 1. How does changing the choice of area vector affect the sign of the encircled current? 2. How does changing the choice of a clockwise or counterclockwise path affect the sign of the line integral? 3. To make the sign of Ampere's law consistent on both sides of the equation, which direction should be used for the line integral if the area vector is out of the page? garen 4. Devise a rule by which you can use your right hand to identify the direction that should be used for the line integral around a loop based on your choice of area vector for the loop. Check the results in your table with a tutorial instructor before continuing. Tutorials in Introductory Physics, Physics Education Group, Department of Physics34 Ampere's law WALPAST II. The line integral of the magnetic field In each case below, a square loop is placed near one or more wires, all carrying the same current I. Consider each line integral of the magnetic field using a counterclockwise path. of the loop. A. Case 1: A single wire with current out of the page passes through the center IO Find the sign of the line integral along each side: Top: Bottom: Left: Right : In the first column of the table below, indicate whether the line integral around the entire loop is positive, negative, or zero. B. Case 2: Two symmetrically placed wires, one with current into the page and O one with current out of the page, pass through the loop. Find the sign of the line integral along each side: Top: Bottom: Left: Right: In the first column of the table below, indicate whether the line integral around the entire loop is positive, negative, or zero. C. Case 3: A single wire with current out of the page is above the loop. Find the sign of the line integral along each side: cool Top: Bottom: Left: Right: Based on your answers above, do you have enough information to determine the sign of the line integral around the entire loop? Explain why or why not. D. Suppose you evaluated the line integral in a clockwise direction instead. In the second column of the table below, indicate the sign of the line integral around each loop in this case If you do not have enough information to fill in a box, leave it blank for now. Do not fill in the last two columns now; you will be asked to do so on the next page. J B . di, taken: Encircled current, with A: TR 9001 Counterclockwise Clockwise Into the page Out of the page Case 1: Case 2: Case 3