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Chapter 29: Q25P (page 858)

A wire with currenti=3.00Ais shown in Figure. Two semi-infinite straight sections, both tangent to the same circle, are connected by a circular arc that has a central angle 胃and runs along the circumference of the circle. The arc and the two straight sections all lie in the same plane. If B=0at the circle鈥檚 center, what is 胃?

Short Answer

Expert verified

The value of 鈭�for the zero magnetic field at the circle鈥檚 center is胃=2.00rad.

Step by step solution

01

Given

  1. The current flowing through the wire is i=3.00A
  2. The magnetic field at the circle鈥檚 center is B=0T.
02

Determine the formulas for the magnetic field as:

Formula:

Bstraight=渭0i4蟺R

Barc=渭0i鈭�4蟺R

03

Calculate the value of ∅  for the zero magnetic field at the circle’s center

The magnetic field due to a current in semi-infinite straight wire is as follows:

Bstraight=渭0i4蟺R

According to the right hand rule, both wires produce a magnetic field that is pointing out of the page.

The magnetic field due to the current in a circular arc of the wire is:

Barc=渭0i鈭�4蟺R

According to the right hand rule, it is pointing into the page.

The total magnetic field for the system is:

B=2Bstraight=Barc

B=2渭0i4蟺R-渭0i鈭�4蟺R

B=2渭0i4蟺R-渭0i鈭�4蟺R

0T=2渭0i4蟺R-渭0i鈭�4蟺R

Solve further as:

2渭0i4蟺R=渭0i鈭�4蟺R

鈭�=2.00rad

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Most popular questions from this chapter

In Fig. 29-54a, wire 1 consists of a circular arc and two radial lengths; it carries currenti1=0.50Ain the direction indicated. Wire 2, shown in cross section, is long, straight, and Perpendicular to the plane of the figure. Its distance from the center of the arc is equal to the radius Rof the arc, and it carries a current i2 that can be varied. The two currents set up a net magnetic fieldB鈬赌at the center of the arc. Figure bgives the square of the field鈥檚 magnitude B2 plotted versus the square ofthe currenti22. The vertical scale is set byBs2=10.0脳10-10T2what angle is subtended by the arc?

Figure 29-85 shows, in cross section, two long parallel wires that are separated by distance d=18.6cm. Each carries 4.23A, out of the page in wire 1 and into the page in wire 2. In unit-vector notation, what is the net magnetic field at point Pat distance R=34.2cm, due to the two currents?

In Fig. 29-4, a wire forms a semicircle of radius R=9.26cmand two (radial) straight segments each of length L=13.1cm. The wire carries current i=34.8mA. What are the(a) magnitude and(b) direction (into or out of the page) of the net magnetic field at the semicircle鈥檚 center of curvature C?

A straight conductor carrying current i=5.0Asplits into identical semicircular arcs as shown in Figure. What is the magnetic field at the center C of the resulting circular loop?

Question: Figure 29-31 shows four arrangements in which long, parallel, equally spaced wires carry equal currents directly into or out of the page. Rank the arrangements according to the magnitude of the net force on the central wire due to the currents in the other wires, greatest first.
See all solutions

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