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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

At a certain location in the Philippines, Earth鈥檚 magnetic field of 39渭罢is 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?

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