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 observing the following: Electrons moving upward feel a magnetic force in the NW direction; Electrons moving horizontally North are pushed down; Electrons moving horizontally South-East are pushed upward. He naturally concludes that the magnetic field at this landing site is in which direction?

Magnetic field is in south west direction .

Explanation:

Let us represent various direction by  i , j, k . i representing east , j representing north and k representing vertically upward direction .

magnetic field is represented vectorially as follows

B = B₀ ( - i - j )

In the first case velocity of electron

v = v k

Force = q ( v x B )

= -e [ vk x B₀ ( - i - j ) ]

= evB₀ ( j -i )

Direction of force is north -west .

In the second case velocity of electron

v = vj

Force = -e [ vj x B₀ ( - i - j ) ]

= - evB₀ k

force is downward

In the third case, velocity of electron

v = v( -j +i )

Force = -e [ v( -j +i ) x B₀ ( - i - j ) ]

= 2 evB₀ k

Force is upward.

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