A particle of charge q and mass m starts from the origin with velocity v⃗=a î. A uniform magnetic field B⃗=(b/4)î+(√3b/4)ĵ exists everywhere. What is the y-component of velocity when the z-coordinate becomes maximum?
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Question

A particle of charge q and mass m starts from the origin with velocity v⃗=a î. A uniform magnetic field B⃗=(b/4)î+(√3b/4)ĵ exists everywhere. What is the y-component of velocity when the z-coordinate becomes maximum?

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G1 Physics · Accepted Answer

Magnetic force changes only the velocity component perpendicular to B; the component parallel to B remains constant. Resolve the initial velocity along and perpendicular to B⃗=(b/4)î+(√3b/4)ĵ. At the instant z is maximum, the rotating perpendicular component gives vᵧ=√3a/2. Hence B.