Question

# An electron moving with a velocity V1=2^i m/s at a point in a magnetic field experiences a force −→F1=−2^j N. If the electron is moving with a velocity →V2=2^j m/s at the same point, it experiences a force −→F2=2^i N. The force electron would experience if it were moving with a velocity →V3=2^k m/s at the same point is

A
Zero
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B
2^k N
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C
2^k N
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D
Information is insufficient
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Solution

## The correct option is A ZeroLet the magnetic field be →B=B ^n We have, →F=q(→V×→B)−2^j=(−e)(2^i×B^n)⇒^j=eB(^i×^n)⇒eB=1 and ^n=−^k (∵^i×^k=^j)⇒→B=1e(−^k) The information about →V2 and −→F2 is redundant and it need not be considered. If considered, it will yeild the same answer as above. If the electron moves with →V3=2^k if will be moving anti-parallel to →B. Thus it will not experience any force.

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