A particle of specific charge α=q/m starts from the origin under E⃗=E₀î and B⃗=B₀k̂. Its velocity at (x₀, y₀,0) is (4î-3ĵ) m/s. The value of x₀ is:
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Question

A particle of specific charge α=q/m starts from the origin under E⃗=E₀î and B⃗=B₀k̂. Its velocity at (x₀,y₀,0) is (4î−3ĵ) m/s. The value of x₀ is:

G1 Physics · Accepted Answer

Magnetic force does no work, so change in kinetic energy comes only from E⃗. Starting from rest, ½mv²=qE₀x₀. At the stated point v²=4²+(−3)²=25 and q/m=α. Hence x₀=25/(2αE₀), option C.