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In Fig.29-64, five long parallel wires in an xy plane are separated by distance d=50.0cm. The currents into the page are i1=2.00A,i3=0.250A,i4=4.00A,andi5=2.00A; the current out of the page is i2=4.00A. What is the magnitude of the net force per unit length acting on wire 3 due to the currents in the other wires?

Short Answer

Expert verified

The magnitude of the net force per unit length acting on wire 3 due to current in the other wires isFL=8.00×10-7N/m

Step by step solution

01

Given

  • Five long parallel wires are separated by distanced=50.0cm
  • The current in wire 1 isi1=2.00A.
  • The current in wire 2 isi2=4.00A.
  • The current in wire 3 isi3=0.250A
  • The current in wire 4 isi4=4.00A
  • The current in wire 5 isi5=2.00A
  • The current into the page arei1, i3,i4, andi5.
  • The current out of the page is i2.
02

Understanding the concept

Using Eq. 29-13 and considering the given summary, we can find the magnitude of net force per unit length acting on wire 3 due to current in the other wires.

Formula:

From Eq. 29-13, the force between two parallel currents is

Fx=μ0Li1i22πd

03

Calculate the magnitude of the net force per unit length acting on wire 3 due to current in the other wires.

From Eq. 29-13, the force between two parallel currents is

Fx=μ0Li1i22πd

Since currents into the page arei1, i3,i4, andi5, wire 3 is, therefore, attached to all but wire 2.

Therefore, from Eq. 29-13, themagnitude of net force per unit length acting on wire 3 due to the current in the other wires is

FL=μ0i32π-i12d+i2d+i4d+i52d

Substituting given values, we get

FL=4π×10-70.2502π-2.0020.500+4.000.500+4.000.500+2.0020.500FL=4π×10-70.2502π16FL=8.00×10-7N/m

Hence, the magnitude of the net force per unit length acting on wire 3 due to current in the other wires is FL=8.00×10-7N/m

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Most popular questions from this chapter

Figure 29-50ashows, in cross section, two long, parallel wires carrying current and separated by distance L. The ratio i1/i2 of their currents is4.00; the directions of the currents are not indicated. Figure 29-50bshows the ycomponent Byof their net magnetic field along the xaxis to the right of wire 2. The vertical scale is set by Bys=4.0nT , and the horizontal scale is set by xs=20.0cm . (a) At what value of x0 is Bymaximum?(b) If i2=3mA, what is the value of that maximum? What is the direction (into or out of the page) of (c) i1 and (d) i2?

In Fig. 29-44, point P2is at perpendicular distanceR=25.1cm from one end of a straight wire of length L=13.6cmcarrying current i=0.693A.(Note that the wire is notlong.) What is the magnitude of the magnetic field at P2?

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.

In Fig. 29-48 part of a long insulated wire carrying currenti=5.78mAis bentinto a circular section of radius R=1.89cm. In unit-vector notation, what is the magnetic field at the center of curvature Cif the circular section (a) lies in the plane of the page as shown and (b) is perpendicular to the plane of the page after being rotated 90°counterclockwise as indicated?

Figure 29-68 shows two closed paths wrapped around two conducting loops carrying currents i1=5.0Aand i2=3.0A.(a) What is the value of the integral B.dsfor path 1 and (b) What is the value of the integral for path 2?

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