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Chapter 29: Q3P (page 836)

At a certain location in the Philippines, Earth’s magnetic field of 39μTis horizontal and directed due north. Suppose the net field is zero exactly8.0cmabove a long, straight, horizontal wire that carries a constant current. (a) What are the magnitude and (b) What is the direction of the current?

Short Answer

Expert verified

a. The magnitude of the current is16A .

b. The direction of the current is east.

Step by step solution

01

Determining the formula for the magnetic field 

Biot- savart law states that the magnetic intensity at any point due to a steady current in an infinitely long straight wire is directly proportional to the current and inversely proportional to the distance from the point to the wire. Using this equation, Solve for current.

Magnetic field due to the current in the wire at a point and distance r from the wire is:

B=μ0i2πr

02

(a) Calculating magnitude of the current  

To find the magnitude of current :

B=μ0i2πr

Substitute the value and solve as:

i=2πrBμ0=2π×0.08×39×10-64π×10-7=16A

03

(b) Calculating the direction of the current 

Direction of the current:

As the field is directed towards south, the current must be directed from west to east as per the right hand rule.

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Most popular questions from this chapter

Question: Two long wires lie in an xyplane, and each carries a current in the positive direction of the xaxis.Wire 1 is at y=10cmand carries role="math" localid="1662817900403" iA=6A; wire 2 is at role="math" localid="1662817917709" y=5cmand carries role="math" localid="1662817934093" iB=10A. (a) In unitvector notation, what is the net magnetic field at the origin? (b) At what value of ydoesrole="math" localid="1662818220108" B→=0? (c) If the current in wire 1 is reversed, at what value of role="math" localid="1662818150179" ydoesB→=0?

Figure 29-52 shows, in cross section, four thin wires that are parallel, straight, and very long. They carry identical currents in the directions indicated. Initially all four wires are atdistanced=15.0cmfrom the origin of the coordinate system, where they create a net magnetic field .(a) To what value of xmust you move wire 1 along the xaxis in order to rotate counter clockwise by 30°? (b) With wire 1 in that new position, to what value of xmust you move wire 3 along the xaxis to rotate by30°back to its initial orientation?

Question: Two long straight thin wires with current lie against an equally long plastic cylinder, at radius R=20.0cmfrom the cylinder’s central axis.

Figure 29-58ashows, in cross section, the cylinder and wire 1 but not wire 2. With wire 2 fixed in place, wire 1 is moved around the cylinder, from angle localid="1663154367897" θ1=0°to angle localid="1663154390159" θ1=180°, through the first and second quadrants of the xycoordinate system. The net magnetic field B→at the center of the cylinder is measured as a function of θ1. Figure 29-58b gives the x component Bxof that field as a function of θ1(the vertical scale is set by Bxs=6.0μT), and Fig. 29-58c gives the y component(the vertical scale is set by Bys=4.0μT). (a) At what angle θ2 is wire 2 located? What are the (b) size and (c) direction (into or out of the page) of the current in wire 1 and the (d) size and (e) direction of the current in wire 2?

A long, hollow, cylindrical conductor (with inner radius 2.0mm and outer radius 4.0mm) carries a current of 24A distributed uniformly across its cross section. A long thin wire that is coaxial with the cylinder carries a current of 24A in the opposite direction. What is the magnitude of the magnetic field (a) 1.0mm,(b) 3.0mm, and (c) 5.0mm from the central axis of the wire and cylinder?

In Figure 29-46 two concentric circular loops of wire carrying current in the same direction lie in the same plane. Loop 1 has radius1.50cm and carries 4.00mA. Loop 2 has radius2.50cmand carries 6.00mA.Loop 2 is to be rotated about a diameter while the net magnetic field B→set up by the two loops at their common center is measured. Through what angle must loop 2 be rotated so that the magnitude of that net field is 100nT?
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