How much from due north with the compass needle be deflected in the following case?
A boat is sailing due north, as indicated by its compass needle, in a location where Earth's magnetic field is 2.0 X 10^-5 T. The boat’s captain inadvertently places his radio on the shelf directly above the compass. If the 5.0 A current carrying wire of the radio is aligned in a north-south direction and is 30 cm directly above the compass, how much from due north with the compass needle be deflected?
The boat is initially sailing due North as indicated by a compass and the Earth's magnetic field is 2.0*10^-5 T. A radio is placed above the compass. There is a current carrying wire in the radio that is aligned in the North-South direction, carries a current of 5 A and is placed 30 cm above the compass needle.
There is a magnetic field created due the current flowing in the wire and at a distance r from the wire is equal to B = C*I/(2*pi*r) where I is the current flowing and C is a constant equal to 4*pi*10^-7 T*m*s/C. Substituting the values given B = (4*pi*10^-7*5)/(2*pi*0.3) = (10^-6)/(0.3)
The net force of the magnetic field of the Earth and the that of the current carrying wire acts in a direction making a angle theta = arc tan((10^-6/(0.6*10^-5))
=> arc tan(1/6)
=> 9.46 degrees