1. The figure below represents a wire that is perpendicular to the page, and surrounded by a circular Amperian path of integration. The current in the wire is equal to 2.0 A, and is directed out of the page.

a) At point P, draw an arrow in the direction of the magnetic field at that point.

b) What is the magnitude of the angle between the magnetic field and the path of integration at point P?

c) What is the value of the integral about the path shown in the picture? Express your answer in terms of m_0.

2. The figure below represents a wire that is perpendicular to the page, and surrounded by a square Amperian path of integration. The current in the wire is equal to 2.0 A, and is directed out of the page.

a) At point P, draw an arrow in the direction of the magnetic field at that point.

b) What is the approximate magnitude of the angle between the magnetic field and the path of integration at point P? Point P is on the vertical section of the path, and just below the corner.

c) What is the value of the integral about the path shown in the picture? Express your answer in terms of m_0.

3. The figure below represents four wires that are perpendicular to the page. Wire A is surrounded by a circular Amperian path of integration, and wire B is surrounded by a square Amperian path of integration. The current in each of the four wires is equal to 2.0 A. The currents in wires A and B are directed into the page, and the currents in the other two wires are directed out of the page.

What is the value of the integral for the circular path around wire A? Express your answer in terms of m₀.

b) What is the value of the integral for the square path around wire B? Express your answer in terms of m₀.

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To explore the ideas of Ampere's Law, we will use a computer simulation that you can access from the Physics II web page. Just click on the HTML title "Ampere's Law", under activities.

When you have reached the program, explore the "Examples" section. You might want to check some of your answers to the previous questions.

4. Use the rectangle path tool on an extended wire. First surround an entire wire, then one half, and finally one quarter of a wire.

a. Explain the result that Ampere's' Law gives in each case.

b. Then go to the "Hidden Wires Exercise". Use the simulation, and answer the questions below.

1) How many wires are in the rectangular area?

2) Give the coordinates of all the hidden wires, and the magnitudes and directions of their currents. For a thick wire, give the coordinates of the approximate center of the wire. The coordinates of the point where the cursor is located appear in the browser's status line at the bottom of the window. If you manage to put the cursor directly on a thin wire, the arrow will disappear, and a small circle will appear there.

3) Indicate which wires are thin wires and which are spread over some finite area.

4) At how many points in the area is the magnetic field equal to zero?

5) Give the approximate coordinates of those points where B = 0.