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?

Short Answer

Expert verified
  1. The magnitude of the magnetic field isB=1.18×10-7T
  2. The direction of the magnetic field is into the page.

Step by step solution

01

Given

  1. Radius of circle isR=9.26cm=9.26×10-2m
  2. Length of each straight segment isrole="math" localid="1663098315135" L=13.1cm=13.1×10-2m
  3. Current isi=34.8mA=34.8×10-3A
02

Determine the formulas

The magnitude of the magnetic field Bat centre of circular arc, of radius R, and central angleϕ, carrying a current Iis given as follows:

B=μIϕ4πR

For a straight conductor consider the formulas:

dB=μ0Ids×r^4πr2

Here,dB¯is the magnetic field through the current carrying conductor,ds¯length of the element andr^is unit vector that is a point from the element to the given point.

Formulae:

B=μIϕ4πRB=μIdssinθ4πr2

03

(a) Calculate the magnitude of the net magnetic field at the semicircle’s center of curvature C

To calculate the magnetic field B1due to current for left straight segment as follows:

B1=μIdssinθ4πr2

θ=0°

So,

B1=0

Calculate the magnetic field B2due to current for a right straight segment as follows:

B2=μIdssinθ4πr2

Here θ=0°

So

B2=0

Calculate the magnetic field B3due to current from circular section as follows

B3=μIϕ4πRB3=4π×10-7N/A2×34.8×10-3A×π4π×9.26×10-2mB3=1.18×10-7T

So, the total magnetic field at the center of semicircle arc is

B=B1+B2+B3=1.18×10-7T

Hence the magnetic field is, 1.18×10-7T.

04

(b) Calculate the direction (into or out of the page) of the net magnetic field at the semicircle’s center of curvature C

Using the right hand rule, direction of magnetic field is into the page

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Most popular questions from this chapter

Figure 29-25 represents a snapshot of the velocity vectors of four electrons near a wire carrying current i. The four velocities have the same magnitude; velocity is directed into the page. Electrons 1 and 2 are at the same distance from the wire, as are electrons 3 and 4. Rank the electrons according to the magnitudes of the magnetic forces on them due to current i, greatest first.

The current-carrying wire loop in Fig. 29-60a lies all in one plane and consists of a semicircle of radius 10.0cm, a smaller semicircle with the same center, and two radial lengths. The smaller semicircle is rotated out of that plane by angleθ, until it is perpendicular to the plane (Fig.29-60b). Figure 29-60c gives the magnitude of the net magnetic field at the center of curvature versus angleθ . The vertical scale is set byBa=10.0μTandBb=12.0μT. What is the radius of the smaller semicircle?

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?

Figure shows a snapshot of a proton moving at velocityv=200msj^toward a long straight wire with current i=350mA. At the instant shown, the proton’s distance from the wire is d=2.89cm. In unit-vector notation, what is the magnetic force on the proton due to the current?

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.

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