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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

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’s center of curvature C?

Question: In Figure, current I=56.2mAis set up in a loop having two radial lengths and two semicircles of radiia=5.72cm andb=9.36cm with a common centerP(a) What are the magnitude and (b) What are the direction (into or out of the page) of the magnetic field at P and the (c) What is the magnitude of the loop’s magnetic dipole moment? and (d) What is the direction of the loop’s magnetic dipole moment?

Figure 29-27 shows cross-sections of two long straight wires; the left-hand wire carries current i1 directly out of the page. If the net magnetic field due to the two currents is to be zero at point P, (a) should the direction of current i2 in the right-hand wire be directly into or out of the page, and (b) should i2 be greater than, less than, or equal to i1?

Eight wires cut the page perpendicularly at the points shown in Figure 29-70 wire labeled with the integer k(k=1,2,...,8)carries the current ki, where i=4.50mA. For those wires with odd k, the current is out of the page; for those with even k, it is into the page. EvaluateB.ds along the closed path in the direction shown.

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?

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