All three wires shown have current I. The current in wire Z is into the page. Th
ID: 2301113 • Letter: A
Question
All three wires shown have current I. The current in wire Z is into the page. The magnetic
fields at the midway points between adjacent wires are indicated.
a. What is the direction of the current in wire X? Explain.
b. What is the direction of the current in wire Y? Explain.
For the situation shown above, describe how each of the following changes will affect the
total magnetic field at the point midway between wires X and Y. In each case, explain
your reasoning.
c. The current in wire Y is reversed.
d. The currents in wires X and Z are doubled.
e. The current in Y goes to zero.
f. The currents in all three wires are reversed.
Explanation / Answer
What is the direction of the current in wire X? Explain.
What is the direction of the current in wire Y? Explain.
The current in wire X is out of the page (the magnetic field due to wire X circles in the counterclockwise direction around the wire) and the current in wire Y is into the page (the magnetic field due to wire Y circles in the clockwise direction around the wire). As shown, the current in wire Z is into the page, so the magnetic field due to wire Z circles in the clockwise direction around wire Z.
Given those directions for the magnetic fields due to the wires, the magnetic field at location R due to all three wires is given by
BR=BX+BY+BZ. At that location, all three fields point up, so the total field is large and directed up.
The magnetic field at location S due to all three wires is given by BS=BX+BY+BZ. At that location, the field due to wire X points up, the field due to wire Y points down, and the field due to wire Z points up. Since wires Y and Z are both equidistant from point S and carry the same current, the fields due to those wires will cancel at point S, leaving the smaller field due to wire X at point S to provide the net magnetic field at S.
For the situation shown above, describe how each of the following changes will affect the total magnetic field at the point midway between wires X and Y. In each case, explain your reasoning.
The current in wire Y is reversed.
The field at location R decreases, but the direction remains the same.
The currents in wires X and Z are doubled.
The field at location R increases, but the direction remains the same.
The current in Y goes to zero.
The field at that location decreases, but the direction remains the same.
The currents in all three wires are reversed.
The magnitude of the field remains the same, but the direction reverses.