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Chapter 29: Q71P (page 862)

A10-gaugebare copper wire ( 2.6 mmin diameter) can carry a current of 50Awithout overheating. For this current, what is the magnitude of the magnetic field at the surface of the wire?

Short Answer

Expert verified

Magnitude of the net magnetic field at the surface of wire is 7.7×10-3 T.

Step by step solution

01

Identification of the given data

  1. The current is, i=50 A.
  2. The diameter is,d=2.6 mm.
02

Understanding the concept

We use the formula of magnetic field due to a long straight wire at perpendicular distancefrom the wire to calculate the magnitude of magnetic field.

Formula:

B=μ0i2πd

03

Calculate the magnitude of the net magnetic field at the surface of the wire

The magnetic field due to the long straight wire at any distance from the wire is given by

B=μ0i2πd

We have to find the magnitude of the magnetic field on the surface of the wire whose distance from the center of wire is Rand given by

B=μ0i2πR

Diameter d=2.6 mmand radius R=2.62 mm=0.0013 m.

Substitute all the value in the above equation.

localid="1664177943519" B=4π×10-7TmA ×50 A2π×0.0013 m

localid="1663008809868" B=7.7×10-3 T

Hence the net magnetic field at the surface of wire is 7.7×10-3 T.

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Most popular questions from this chapter

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.

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.

The current density J→ inside a long, solid, cylindrical wire of radius a=3.1mm is in the direction of the central axis, and its magnitude varies linearly with radial distance rfrom the axis according toJ=J0r/a, where J0=310A/m2. (a) Find the magnitude of the magnetic field at role="math" localid="1663132348934" r=0, (b) Find the magnitude of the magnetic fieldr=a/2 , and(c) Find the magnitude of the magnetic field r=a.

In Figure, five long parallel wires in an xyplane are separated by distanced=8.00cm, have lengths of10.0 m,and carry identical currents of3.00 Aout of the page. Each wire experiences a magnetic force due to the other wires. In unit-vector notation,(a) What is the net magnetic force on wire 1, (b) What is the net magnetic force on wire 2, (c) What is the net magnetic force on wire 3, (d) What is the net magnetic force on wire 4, and (e) What is the net magnetic force on wire 5?

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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