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Question

# An electron beam passes through a magnetic field of 2×10−3Wb/m2 and an electric field of 1.0×104V/m both acting simultaneously. The path of electron remains undeviating. The speed of electron if the electric field is removed, and the radius of electron path will be respectively.

A
10×106m/s,2.43
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B
2.5×106m/s,0.43
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C
5×106m/s,1.43
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D
None of these
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Solution

## The correct option is C 5×106m/s,1.43B=2×10−3Wb/m2,E=1×104V/m2Since the path of electron remains undeviated, qvB=qE or v=EB=1×10+42×10−3=0.5×107=5×106m/sIf the electric field is removed, the path of the charged particle is circular and magnetic field provides the necessary centripetal force, i.e.,mv2r=Bev⇒r=mvBe=9.1×10−31×5×1062×10−3×1.6×10−19=14.3×10−3m=1.43cm

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