A compass needle points 19 E of N outdoors However when it i

A compass needle points 19 E of N outdoors. However, when it is placed 16.0 cm to the east of a vertical wire inside a building, it points 29 E of N. The Earth\'s field is the same at both positions of the compass, it is 0.50×104T and is horizontal.

What is the magnitude of the current in the wire?

Solution

Bsin(thetha2) = Bearth*sin(thetha1)

Bcos(thetha2) = Bearth*cos(thetha1) - Bwire

=> B wire = 0.50*10^-4*( cos(19) - sin(19)/(tan(29)) = 0.50*10^-4*(0.945 - 0.325/0.5543) = 0.00001793 T = 1.79*10^-5 T

Bwire = uo*2I/(4pir)

=> 0.00001793 = 10^-7*(2*I/(0.16)

=> I = 14.34 A