A particle of mass m and charge q is thrown from origin at t = 0 with velocity 2î + 3ĵ + 4k̂ units in a region with uniform magnetic field B⃗⃗= 2î units. After time t = πm qB , an electric field E⃗⃗ is switched on such that particle moves on a straight line with constant speed. E⃗⃗ may be :-
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Question

A particle of mass m and charge q is thrown from origin at t = 0 with velocity 2î + 3ĵ + 4k̂ units in a region with uniform magnetic field B⃗⃗= 2î units. After time t = πm qB , an electric field E⃗⃗ is switched on such that particle moves on a straight line with constant speed. E⃗⃗ may be :-

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G1 Physics · Accepted Answer

E must cancel the magnetic force at the switching instant: E⃗=−v⃗×B⃗. Evolving the perpendicular velocity for t=πm/(qB) reverses its j-k components; substitution gives E⃗=−6k̂+8ĵ. Hence C.