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Question

A uniform magnetic field B=Bx^i+By^j+Bz^k and uniform electric field E=Er^i+Ey^j+Ez^k exists in a space. A particle enters the region with initial velocity u=ux^i+uy^j+uz^k. If u×B=0 and u×E=0, the path of charged particle will be:

A
Cricle
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B
Helix with uniform pitch
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C
Straight line
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D
Helix with variable pitch
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Solution

The correct option is C Straight line
If u×B=0, it means that velocity and magnetic field are parallel, or antiparallel (θ=0 or π).

If u×E=0, it means that velocity and electric field are parallel or antiparallel (θ=0 or π)

Hence, we conclude that u,E and B will be in either same or opposite direction.

Path of particle will be straight line as only electric force will act and Fmagnetic=0

Hence, option(c) is the correct answer.

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