Question

Figure 29-26 shows four arrangements in which long parallel wires carry equal currents directly into or out of the page at the corners of identical squares. Rank the arrangements according to the magnitude of the net magnetic field at the center of the square, greatest first.

Short answer

The ranking of arrangements according to the magnitude of the net magnetic field at the center of the square is $\mathrm{c}>\mathrm{d}>\mathrm{a}=\mathrm{b}.$

Step-by-step solution

Step 1: Given

Figure showing four arrangements in which long parallel wires carry equal currents directly into or out of the page.

Determining the concept

Use the concept of magnetic field and current to determine the magnitude of the net magnetic field at the center of the square.

Determining the arrangements according to the magnitude of the net magnetic field at the center of the square, greatest first.

The magnetic field depends directly on the current and the net through the arrangement.

From the given figure it can be interpreted that,

a. In arrangement (a) since current directed into page and out of page are in oppositely directions, they get cancelled out, and hence, the net magnetic field is zero.

b. Similarly, in arrangement (b); the net magnetic field is zero.

c. In arrangement (c); the two currents directing into page and two out of page are on the same side, so they get added.

d. In arrangement (d), the two currents are oppositely directed and two are in the same direction that is out of the page.

Hence, the ranking of arrangements according to the magnitude of the net magnetic field at the center of the square is,$\mathrm{c}>\mathrm{d}>\mathrm{a}=\mathrm{b}$

Therefore, magnetic field depends on net current through the wire.