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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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