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?

Expert Answers

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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

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