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Chapter 29: Q59P (page 861)

What is the magnitude of the magnetic dipole moment μ→ of the solenoid described in Problem 51?

Short Answer

Expert verified

The magnitude of the magnetic dipole moment is0.46 A⋅m2.

Step by step solution

01

Listing the given quantities:

The length,l=25  cm=0.25m

The diameter,d=10  cm=0.10m

The number of turns,N=200

The current,i=0.29 A

02

Understanding the concept of magnetic field:

The magnitude of the magnetic dipole moment can be defined as the product of number of turns, current in that loop, and the area of that loop. Using this concept, you can calculate the magnitude of the magnetic dipole moment.

Formula:

The magnetic dipole moment is,

μ=NiA

Here, Nis the number of turns,i is the current,A is the area.

03

Calculations of the magnitude of the magnetic dipole moment:

To calculate the radius of the loop as

R=d2=0.10m2=0.05m

Now the magnetic dipole moment is given by,

μ=NiA=NiπR2=200×0.29A×3.14×(0.05m)2=0.46 A⋅m2

Hence, the magnitude of the magnetic dipole moment is 0.46 A⋅m2.

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Most popular questions from this chapter

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→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=-0.627μN/masx→∞.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?

A long wire carrying 100A is perpendicular to the magnetic field lines of a uniform magnetic field of magnitude 5.0 mT. At what distance from the wire is the net magnetic field equal to zero?

A surveyor is using a magnetic compass 6.1m below a power line in which there is a steady current of 100A .(a) What is the magnetic field at the site of the compass due to the power line? (b) Will this field interfere seriously with the compass reading? The horizontal component of Earth’s magnetic field at the site is role="math" localid="1663130453654" 20mT .

Figure 29-89 is an idealized schematic drawing of a rail gun. Projectile Psits between two wide rails of circular cross section; a source of current sends current through the rails and through the(conducting) projectile (a fuse is not used). (a) Let wbe the distance between the rails, Rthe radius of each rail, and i the current. Show that the force on the projectile is directed to the right along the rails and is given approximately byF→=i2μ02π·ln(w+RR)

(b) If the projectile starts from the left end of the rails at rest, find the speed vat which it is expelled at the right. Assume that I = 450 kA, w = 12 mm, R = 6.7 cm, L = 4.0 m, and the projectile mass is 10 g.

A solenoid 1.30 long and2.60cm in diameter carries a current of 1.80A. The magnetic field inside the solenoid is 23.0mT . Find the length of the wire forming the solenoid.
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