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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

Question: Figure 29-72 shows an arrangement known as a Helmholtz coil. It consists of two circular coaxial coils, each of200turnsand radiusR=25.0cm, separated by a distances=R. The two coils carry equal currentsi=12.2mAin the same direction. Find the magnitude of the net magnetic field at P, midway between the coils.

In a particular region there is a uniform current density of 15A/m2in the positive z direction. What is the value of 鈭�B.dswhen that line integral is calculated along the three straight-line segments from (x, y, z) coordinates (4d, 0, 0) to (4d, 3d, 0) to (0, 0, 0) to (4d, 0, 0), where d=20cm?

Figure a shows, in cross section, three current-carrying wires that are long, straight, and parallel to one another. Wires 1 and 2 are fixed in place on an xaxis, with separation d. Wire 1 has a current of0.750A, but the direction of the current is not given. Wire 3, with a current of0.250Aout of the page, can be moved along the xaxis to the right of wire 2. As wire 3 is moved, the magnitude of the net magnetic forceF鈫�2on wire 2 due to the currents in wires 1 and 3 changes. The xcomponent of that force is F2xand the value per unit length of wire 2 isF2x/L2. Figure bgivesF2x/L2versus the position xof wire 3. The plot has an asymptoteF2xL2=-0.627渭N/masx鈫�鈭�.The horizontal scale is set byxs=12.0cm. (a) What are the size of the current in wire 2 and (b) What is the direction (into or out of the page) of the current in wire 2?

In Fig. 29-83, two infinitely long wires carry equal currents i. Each follows a 90掳arc on the circumference of the same circle of radius R. Show that the magnetic field B鈫�at the center of the circle is the same as the field B鈫�a distance R below an infinite straight wire carrying a current Ito the left.

Question:In Figure, four long straight wires are perpendicular to the page, and their cross sections form a square of edge length a=20cm. The currents are out of the page in wires 1 and 4 and into the page in wires 2 and 3, and each wire carries 20 A. In unit-vector notation, what is the net magnetic field at the square鈥檚 center?
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