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Question

A uniform and constant magnetic field B=^zB exists in the ^z direction in vacuum. A particle of mass m with a small charge q is introduced into this region with an initial velocity v=^xvx+^zvz. Given that B, m, q, vx andvz are all non-zero. Which one of the following describes the eventual trajectory of the particle?

A
Helical motion in the ^z direction.
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B
Circular motion in the xy plane
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C
Linear motion in the ^z direction
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D
Linear motion in the ^x direction.
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Solution

The correct option is A Helical motion in the ^z direction.

Ans : (a)

Baz = magnetic field
vxax+vzaz=velocity
F = Q(v×B) by Lorentz's law
= Q((vxax+vzaz)×Baz)

Fy=QVx.B(ay)

This results in a circular path in the XY plane with vzaz component causing a linear path.
Both result in a helical path along Z axis


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