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Question

A charged particle goes undeflected in a region of space containing an electric field E and a magnetic field of intensity B. Which of the following is possible?

A
E is parallel to B but v is perpendicular to E
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B
E is parallel to B and v parallel to E
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C
E is perpendicular to B and v is parallel to E×B
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D
E is perpendicualar to B and v is parallel to E.B
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Solution

The correct options are
B E is parallel to B and v parallel to E
C E is perpendicular to B and v is parallel to E×B
From Lorentz force,
FL=Fe+Fm
Fe = electric force
Fm = magnetic force
FL=qE+q(v×B)

If E||B and v||E, then v must be parallel to B.
FL=qE+0=qE
Charge will either accelerate or decelerate in the same direction of v, but does not deflect.

If E is perpendicular to B and v is parallel to E×B
E, B and v are mutually perpendicular to each other.
v×B=kE

FL=qE+q(v×B)
FL=qE+qkE
For k=1,FL=0
Hence, its possible for charge to travel undeflected.

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