Question

nt FULL SCREEN PRINTER VERSION NEXT Cnapter 41, ProDiem b2 A smail compass is held horizontally, the center of its needle a distance of 0.240 m directly north of a long wire that is perpendicular to the earth's surface. When there is no current in the wire, the compass needle points due north, which is the direction of the horizontal component of the earth's magnetic field at that location. This component is paraliel to the earth's surface. When the current in the wire is 39.0 A, the needle points 35.0° east of north. (a) What direction does the current in the wire flow, toward or away from the earth's surface? (b) What is the magnitude of the horizontal component of the earth's magnetic field at the location of the compass? North WPE-East (b) Number Units

Answer 1

a)

From Right Hand rule ,the direction of current is towards the earth's surface

b)

Since

$tan\theta =\frac{ B}{B_{E}}$

Magnetic field due to long straight wire is

B=u_OI/2pir

$B_{E} =\frac{ B}{tan\theta } =\frac{\mu _{o}I}{2\pi r tan\theta }$

$B_{E} = \frac{(4\pi \times 10^{-7})(39)}{2\pi(0.24) tan35 }=4.64\times 10^{-5}T$