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Chapter 29: Q4P (page 856)

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?

Short Answer

Expert verified

The magnetic field at the center isB=0.

Step by step solution

01

Given Information

Angle made by arc=π

02

Determining the formula for the magnetic field

Formula:

Magnetic field at center of circular arc is given by:

BC=μ04π×iϕR

Here, ϕis the angle of arc and R is the radius of the arc.

03

Calculating the magnetic field at the center C of the resulting circular loop 

Magnetic field at center due to arc is given by:

B=μ04π×iϕR

Fields due to both arcs are opposite to each other.

Angle due to semicircular arcs =π,

Net field due to both semicircular arcs is

B=μ04π×iπR+μ04π×i-πR

B=0

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Most popular questions from this chapter

Question: In Fig 29-55, two long straight wires (shown in cross section) carry currentsi1=30.0mAandi1=40.0mAdirectly out of the page. They are equal distances from the origin, where they set up a magnetic field. To what value must current i1be changed in order to rotate20.0°clockwise?

Figure 29-45 shows two current segments. The lower segment carries a current of i1=0.40Aand includes a semicircular arc with radius 5.0cm, angle 180°, and center point P. The upper segment carries current i2=2i1and includes a circular arc with radius 4.0cm, angle 120°, and the same center point P. What are the(a) magnitude and (b) direction of the net magnetic field at Pfor the indicated current directions? What are the (c)magnitude of if i1 is reversed and (d) direction B→ of if i1 is reversed?

Figure 29-80 shows a cross-section of a long cylindrical conductor of radius a=4 cmcontaining a long cylindrical hole of radiusb=1.50cm. The central axes of the cylinder and hole are parallel and are distanced=2cmapart; currentis uniformly distributed over the tinted area. (a) What is the magnitude of the magnetic field at the center of the hole? (b) Discuss the two special casesb=0andd=0.

Three long wires are parallel to a zaxis, and each carries a current ofi=10Ain the positive zdirection. Their points of intersection with the xy plane form an equilateral triangle with sides of 50cm, as shown in Fig. 29-78. A fourth wire (wire b) passes through the midpoint of the base of the triangle and is parallel to the other three wires. If the net magnetic force on wire ais zero, what are the (a) size and (b) direction ( + z or- z)of the current in wireb?

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.
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