A magnetic field is aligned along the positive direction of the y-axis. When ins

Question

A magnetic field is aligned along the positive direction of the y-axis. When inside such field:
(1) What is the direction of the magnetic force acting on a positive charge moving along the negative direction of the z-axis?
(2) What is the direction of the magnetic force acting on a negative charge moving along the positive direction of the x-axis?
(3) What is the direction of the magnetic force acting on a positive charge moving along the negative direction of the y-axis?
(4) In which direction should a positive charge move in order to feel a magnetic force along the negative direction of the x-axis?
(5) In which direction should a negative charge move in order to feel a magnetic force along the positive direction of the z-axis?

Explanation / Answer

Force on a moving charge is given by F = q(v X B). Since force is a cross product of v and B Hence direction of F will be perpendicular to both v and B. If you curl your fingers from v direction to B direction the thumb will give direction of force.

a) Given v = -Vo k and B = Bo j

F = q(-Vo k X Bo j) = qVoBo i (since k X j = -i) Hence force will act in positive x-direction)

b)

Given v = Vo i and B = Bo j

F = -q(Vo i X Bo j) = -qVoBo k (since i X j = k) Hence force will act in negative z-direction)

c)

Given v = -Vo j and B = Bo j

F = q(-Vo j X Bo j) = 0 (since j X j = 0) No force acting on charge.

d)

Given F = -Fo i and B = Bo j

Since k X j = -i Hence positive charge should move in positive z-direction.

5)

Given F = Fo k and B = Bo j

Since i X j = k positive charge should move in positive x-direction. which means negative charge should move in negative x-direction.

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