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Chapter 29: Q21P (page 858)

Figure 29-49 shows two very long straight wires (in cross section) that each carry a current of4.00A directly out of the page. Distance d1=6.00m and distance d2=4.00m. What is the magnitude of the net magnetic field at point P, which lies on a perpendicular bisector to the wires?

Short Answer

Expert verified

Magnitude of the net magnetic field at point P is 256nT.

Step by step solution

01

Given

  1. Permeability of free space, 渭0=4蟺脳10-7TmA.
  2. d1=6.00m.
  3. d2=4.00m.
  4. Current carried by wire,i=4.00A.
02

Understanding the concept

By using the concept of magnetic field due to long wire carrying current and component of magnetic field, determine the net magnetic field at point P.

Formula:

Magnetic field due to the wire at point P is

B=渭0i2蟺r

Here, i=current, 渭0=permeability of free space,r=distance of wire.

03

Calculate the magnitude of the net magnetic field at point P.

First of all, we have to find the r.

By using Pythagoras theorem, solve as:

r=d122+d22

r=622+42

r=25r=5.00m

Now, the magnetic field is given by

B=渭0i2蟺r

B=4蟺脳10-7脳4.02脳3.14脳5.00

B=1.6脳10-7T

B=160nT

The component of the magnetic field cancels with each other, so the magnetic field at point P is

Bp=2Bsin胃

Here,

sin胃=d2r=4.005.00=0.8

Bp=2脳160脳0.8

Bp=256nT

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Most popular questions from this chapter

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鈫�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?

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掳clockwise?

A long vertical wire carries an unknown current. Coaxial with the wire is a long, thin, cylindrical conducting surface that carries a current of30鈥�mAupward. The cylindrical surface has a radius of3.0鈥�mm. If the magnitude of the magnetic field at a point5.0鈥�mmfrom the wire is1.0渭罢, (a) What are the size and(b) What is the direction of the current in the wire?

Figure 29-29 gives, as a function of radial distance r, the magnitude Bof the magnetic field inside and outside four wires (a, b, c, and d), each of which carries a current that is uniformly distributed across the wire鈥檚 cross section. Overlapping portions of the plots (drawn slightly separated) are indicated by double labels. Rank the wires according to (a) radius, (b) the magnitude of the magnetic field on the surface, and (c) the value of the current, greatest first. (d) Is the magnitude of the current density in wire agreater than, less than, or equal to that in wire c?

In Figure, two long straight wires are perpendicular to the page and separated by distance d1=0.75cm. Wire 1 carries 6.5Ainto the page. What are (a) magnitude and (b) direction (into or out of the page) of the current in wire 2 if the net magnetic field due to the two currents is zero at point P located at distance d2=1.50cmfrom wire 2?
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