a electrons beam is moving horizontally from south to north in the vertical component of the earth magnetic field directed downward .in which dieecrion will the beam be deflected

Dear student,

Applying right-hand rule for the cross product of vectors, we find that the direction of v x B is towards east.
Since,
F=-e(v×B)
therefore, th
e beam will be deflected towards opposite to east as given by the formula.
So the beam will be deflected towards west.

Regards

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South to north it deflects towards the west ...
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