First slide

Force on a charged particle moving in a magnetic field

Question

A charged particle is moving in a region where a uniform gravitational field and uniform magnetic field exist (Electric field is zero). Then path of the particle may be

Difficult

A

a straight line
B

a parabola
C

a helic
D

both (1) and (3) are correct

Solution

If the magnetic field is vertically down ward or vertically upward and the particle is projected vertically down ward or vertically upward. Then magnetic force $(\vec{F} = Q \vec{V} \times \vec{B})$ is zero and the path is a vertical straight line. If the particle is projected vertically and the magnetic field is horizontal then the path is a helix of variable pitch.
For parabolic path acceleration of the particle must be constant. But if both gravitational field $(\vec{g})$ and magnetic field $(\vec{B})$ exist and $\vec{B}$ is not parallel to $\vec{g}$ then acceleration of the particle cannot remain constant.

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