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Chapter 29: Q3Q (page 855)

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

Expert verified

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

Step by step solution

01

Step 1: Given

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

02

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.

03

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,c>d>a=b

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

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Most popular questions from this chapter

Question: Two long straight thin wires with current lie against an equally long plastic cylinder, at radius R=20.0cmfrom the cylinder鈥檚 central axis.

Figure 29-58ashows, in cross section, the cylinder and wire 1 but not wire 2. With wire 2 fixed in place, wire 1 is moved around the cylinder, from angle localid="1663154367897" 胃1=0掳to angle localid="1663154390159" 胃1=180掳, through the first and second quadrants of the xycoordinate system. The net magnetic field B鈫�at the center of the cylinder is measured as a function of 胃1. Figure 29-58b gives the x component Bxof that field as a function of 胃1(the vertical scale is set by Bxs=6.0渭T), and Fig. 29-58c gives the y component(the vertical scale is set by Bys=4.0渭T). (a) At what angle 胃2 is wire 2 located? What are the (b) size and (c) direction (into or out of the page) of the current in wire 1 and the (d) size and (e) direction of the current in wire 2?

Question: In Fig 29-76 a conductor carries6.0Aalong the closed path abcdefgharunning along 8of the 12edges of a cube of edge length 10cm. (a)Taking the path to be a combination of three square current loops (bcfgb, abgha, and cdefc), find the net magnetic moment of the path in unit-vector notation.(b) What is the magnitude of the net magnetic field at the xyzcoordinates of(0,5.0m,0)?

Question: In Fig. 29-77, a closed loop carries current 200mA. The loop consists of two radial straight wires and two concentric circular arcs of radii 2.0mand 4.0m. The angle is role="math" localid="1662809179609" 胃=蟺4rad. What are the (a) magnitude and (b) direction (into or out of the page) of the net magnetic field at the center of curvature P?

Figure 29-87 shows a cross section of a hollow cylindrical conductor of radii aand b, carrying a uniformly distributed currenti. (a) Show that the magnetic field magnitude B(r) for the radial distancer in the rangeb<r<ais given byB=渭0i2蟺ra2-b2路(r2-b2)r

(b) Show that when r = a, this equation gives the magnetic field magnitude Bat the surface of a long straight wire carrying current i; when r = b, it gives zero magnetic field; and when b = 0, it gives the magnetic field inside a solid conductor of radius acarrying current i. (c) Assume that a = 2.0 cm, b = 1,8 cm, and i = 100 A, and then plot B(r) for the range 0<r<6.0cm .

A student makes a short electromagnet by winding of wire 300turnsaround a wooden cylinder of diameterd=5.0cm. The coil is connected to a battery producing a current of4.0Ain the wire. (a) What is the magnitude of the magnetic dipole moment of this device? (b) At what axial distance d will the magnetic field have the magnitude5.0渭罢(approximately one-tenth that of Earth鈥檚 magnetic field)?
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