Question

Two long parallel wires carry currents of $20.0A$ and $10.0A$ in opposite directions (Figure). Which of the following statements is true? More than one statement may be correct.

• A. In region I, the magnetic field is into the page and is never zero
• B. In region I, the magnetic field is into the page and is never zero.
• C. In region III, it is possible for the field to be zero.
• D. In region I, the magnetic field is out of the page and is never zero.
• E. There are no points where the field is zero.

Answer 1

Answer: (C), (D)

In region III, it is possible for the field to be zero.
In region I, the magnetic field is out of the page and is never zero.

Any point in region I is closer to the upper wire, which carries the larger current. At all points in this region, the outward directed field due the upper wire will have a greater magnitude than will the inward directed field due to the lower wire. Thus, the resultant field in region I will be nonzero and out of the page, meaning that choice (d) is a true statement and choice (a) is false. In region II, the field due to each wire is directed into the page, so their magnitudes add and the resultant field cannot be zero at any point in this region. This means that choice (b) is false. In region III, the field due to the upper wire is directed into the page while that due to the lower wire is out of the page. Since points in this region are closer to the wire carrying the smaller current, there are points in this region where the magnitudes of the oppositely directed fields due to the two wires will have equal magnitudes, canceling each other and producing a zero resultant field. Thus, choice (c) is true and choice (e) is false.