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Chapter 29: Q3P (page 836)

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?

Short Answer

Expert verified

a. The magnitude of the current is16A .

b. The direction of the current is east.

Step by step solution

01

Determining the formula for the magnetic field 

Biot- savart law states that the magnetic intensity at any point due to a steady current in an infinitely long straight wire is directly proportional to the current and inversely proportional to the distance from the point to the wire. Using this equation, Solve for current.

Magnetic field due to the current in the wire at a point and distance r from the wire is:

B=渭0i2蟺谤

02

(a) Calculating magnitude of the current  

To find the magnitude of current :

B=渭0i2蟺r

Substitute the value and solve as:

i=2蟺rB渭0=2蟺脳0.08脳39脳10-64蟺脳10-7=16A

03

(b) Calculating the direction of the current 

Direction of the current:

As the field is directed towards south, the current must be directed from west to east as per the right hand rule.

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Most popular questions from this chapter

Figure 29-88 shows a cross section of a long conducting coaxial cable and gives its radii (a,b,c). Equal but opposite currents iare uniformly distributed in the two conductors. Derive expressions for B (r) with radial distance rin the ranges (a) r < c, (b) c< r <b , (c) b < r < a, and (d) r > a . (e) Test these expressions for all the special cases that occur to you. (f) Assume that a = 2.0 cm, b = 1.8 cm, c = 0.40 cm, and i = 120 A and plot the function B (r) over the range 0 < r < 3 cm .

Figure 29-68 shows two closed paths wrapped around two conducting loops carrying currents i1=5.0Aand i2=3.0A.(a) What is the value of the integral 鈭�B鈫�.ds鈫�for path 1 and (b) What is the value of the integral for path 2?

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鈥檚 magnetic field at the site is role="math" localid="1663130453654" 20mT .

Question: In Figure, current I=56.2mAis set up in a loop having two radial lengths and two semicircles of radiia=5.72cm andb=9.36cm with a common centerP(a) What are the magnitude and (b) What are the direction (into or out of the page) of the magnetic field at P and the (c) What is the magnitude of the loop鈥檚 magnetic dipole moment? and (d) What is the direction of the loop鈥檚 magnetic dipole moment?

Figure 29-87 shows a cross section of a hollow cylindrical conductor of radii aand b, carrying a uniformly distributed currenti. (a) Show that the magnetic field magnitude B(r) for the radial distancer in the rangeb<r<ais given byB=渭0i2蟺ra2-b2路(r2-b2)r

(b) Show that when r = a, this equation gives the magnetic field magnitude Bat the surface of a long straight wire carrying current i; when r = b, it gives zero magnetic field; and when b = 0, it gives the magnetic field inside a solid conductor of radius acarrying current i. (c) Assume that a = 2.0 cm, b = 1,8 cm, and i = 100 A, and then plot B(r) for the range 0<r<6.0cm .
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