   Chapter 19, Problem 18CQ

Chapter
Section
Textbook Problem

Two long, straight wires cross each other at right angles, and each carries the same current as in Figure CQ19.18. Which of the following statements are true regarding the total magnetic field at the various points due to the two wires? (There may be more than one correct statement.) (a) The field is strongest at points B and D. (b) The field is strongest at points A and C. (c) The field is out of the page at point B and into the page at point D. (d) The field is out of the page at point C and out of the page at point D. (e) The field has the same magnitude at all four points. Figure CQ19.18

To determine
Which of the following statements are correct.

Explanation

The direction of the magnetic field of a long straight wire can be determined as follows: Hold the wire in the right hand pointing the thumb in the direction of the current. The direction in which the fingers of the right hand curl is the direction of the magnetic field.

The system of the two wires is shown in the following figure.

At the point A the magnetic field due to the horizontal wire is directed out of the page and the field due to the vertical wire is into the page.

At the point B the magnetic field due to the horizontal wire is directed out of the page and the field due to the vertical wire is out of the page.

At the point C the magnetic field due to the horizontal wire is directed into the page and the field due to the vertical wire is out of the page.

At the point D the magnetic field due to the horizontal wire is directed into the page and the field due to the vertical wire is into the page.

Conclusion:

Since at points B and D the field due to both the wires point in the same direction, the magnetic field at points B and D will be the strongest

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