Book: Matter and Interaction 4th edition by Chabay and Sherwood question from ch

Question

Book: Matter and Interaction 4th edition by Chabay and Sherwood question from chapter 17.

A long current-carrying wire, oriented North-South, lies on a table (it is connected to batteries which are not shown). A compass lies on top of the wire, with the compass needle about 3 mm above the wire. With the current running, the compass deflects 10 degrees to the West. At this location, the horizontal component of the Earth's magnetic field is about 2e-5 tesla. BI- What is the magnitude of the magnetic field at location A, on the table top, a distance 2.9 cm to the East of the wire, due only to the current in the wire? What is the direction of the magnetic field at location A, due only to the current in the wire-Select- tesla

Explanation / Answer

part (1)
Given that
r = 3 mm,
thita = 10 degree
Be = 2*10^-5 T

the magnitude of the magnetic field at the compass due only to the current I in the wire is
B = u0*I/(2*pi*r), with direction to the west

so the current is to the south.

B/Be = tan(thita)

B = Be*tan(thita)

u0*I/(2*pi*r) = Be*tan(thita)

u0*I/(2*pi) = Be*r*tan(thita)

What is the magnitude of the magnetic field at location A,on the table top,
a distance d = 2.9cm to the East of the wire, due only to the current in the wire

BA = u0*I/(2*pi*d)

= Be*r*tan(thita)/d

= (2*10^-5)*(3)*tan(10)/(2.9)

= 3.648*10^-7 T

part (2)
use right hand rule and determine that the direction of the magnetic field at location A, due only to the current in the wire is toward the ceiling.

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