Question

A straight 1.20 m long conductor has a 2.00 A current travelling toward the East. Earth's magnetic field in this location is 4.90 × 10-5 T [N]. What is the magnetic force on the wire (include both magnitude and direction)?

Answer 1

Answer:

Force's magnitude$=1.176\,10^{-4}\,N$

Direction: down (towards the center of the Earth)

Explanation:

Recall that the magnetic force on a conductor of length L carrying a current I in a magnetic field B is given by the equation: $F=I\,L\,B$ in the case the magnetic field B and the direction of the current are at 90 degrees from each other (which is our case). The direction of the force will be given by the "right hand rule" associated with the vector product that defines this force.

Since the current is moving East, and the magnetic field of the Earth goes from North to South, the resultant Force vector will be pointing towards the Earth (and perpendicular to the plane defined by the current's direction and the magnetic field B)

The magnitude of the force, is given by the formula above, and given that all quantities to be considered are is SI units, it will result in Newtons (N):

$F=I\,L\,B\\F=2\,*\,1.2\,*\,4.9\,10^{-5}\,N\\F=1.176\,10^{-4}\,N$