EM Ampere's law 37 III. Applications of Ampere's law A. A large conducting sheet carries current out of the page. We can model this sheet as a row of parallel wires, each with a current /, shown below. The density of wires (number of wires per unit length) is n. A square Amperian loop with length L is centered on the sheet. Many wires pass through the loop. 1. In terms of n and other relevant quantities, how much current is encircled by the Amperian loop? 2. Sketch magnetic field lines on both sides of the sheet. Use the principle of superposition to determine your answer. 3. Let BL and BR represent the magnitudes of the magnetic field at the left and right sides of the square, respectively How do BL and BR compare? Explain your reasoning. + . Along which of the sides of the Amperian loop is there a non-zero line integral? Explain using a sketch that shows the orientation of the magnetic field vector and the line element vector dl. Write an expression for the line integral around the entire loop in terms of L, BL, and BR. Use the relationship between BL and BR to simplify your expression for the line integral around the entire loop. 5. Ampere's law relates the line integral around an Amperian loop (which you found in part 4) to the net current encircled by the loop (which you found in part 1). Use this relationship to find the magnitude of the magnetic field at the left side of the square in terms of I. What is the magnetic field at the right side of the Amperian loop? Does the magnetic field near a large sheet of current depend on the distance from the sheet? Use your results above to justify your