Each of the current-carrying wires in the figure (Figure 1) is long and straight

Question

Each of the current-carrying wires in the figure (Figure 1) is long and straight, and carries the current I either into or out of the page, as shown.

Part A

What is the direction of the net magnetic field produced by these four wires at the center of the square?

Conceptual Exercise 22.67 Each of the current-carrying wires in the figure (Figure 1) is long and straight, and carries the current I either into or out of the page, as shown v of 1 Figure 1 Part A What is the direction of the net magnetic field produced by these four wires at the center of the square? 45 from the positive z-axis Submit My Answers Give U incorrect; Try Again; 4 attempts remaining

Explanation / Answer

here

B1 = magnetic field due to wire 1

B2 = magnetic field due to wire 2

B3 = magnetic field due to wire 3

B4 = magnetic field due to wire 4

The center of the square is equidistant from all four wires. Thus, at the center of the square, the magnetic field produced by each wire has equal magnitude. Now consider the directions of each magnetic field. If we apply the right-hand rule to wires 2 and 4, we see that they produce magnetic fields at the center of the square that point toward wire 3. On the other hand, the right hand rule shows that the magnetic fields produced by wires 1 and 3 at the center of the square cancel one another.

It follows that the total (net) magnetic field at the center of the square points toward wire 3

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