After landing on an unexplored Klingon planet, Spock tests for the direction of the magnetic field by firing a beam of electrons in various directions and by recording the following observations:1. Electrons moving upward feel a magnetic force in the northwest direction.2. Electrons moving horizontally toward the north are pushed downward.3. Electrons moving horizontally toward the southeast are pushed upward. Mr. Spock therefore concludes that the magnetic field at this landing site is in which direction?A) toward the eastB) toward the northeastC) toward the southwestD) toward the southeastE) toward the west

the correct one is C,

Explanation:

The magnetic force is given by the expression

        F = q v x B

where the bold letters indicate vectors, we can find the modulus of this expression

         F = q v B sin θ

The direction of the to the force with the rule of the right hand. The thumb applies in the direction of the speed, the fingers extended in the direction of the magnetic field and if the charge is positive the palm is in the direction of the force, if the charge is megative the force is in the opposite direction to the palm of hand.

Let's analyze the different situations presented; As the particles emitted are electrons, their charge is negative.

Situation 1. The thumb points upwards, the force is towards the NW as the charge is negative, the palm points towards the SE therefore the finger points towards the SOUTHWEST which must be the direction of the magnetic field

Situation 2. the electrons go horizontally to the north the thumb points in this direction, the force is downwards, therefore the palm points upwards, the extended fingers point to the WEST

Situation 3. the thumb points to the SE towards where the electrons move, the force is upwards the palm points to the SW, therefore the fingers extended points SOUTHWEST

As a result of situations 1 and 3 the magnetic field must point in the SOUTHWEST direction.

Situation 2 gives a different result because the component of the field that is directed to the south does not create exerts and therefore cannot be detected.

When checking the answers, the correct one is C