A proton moves with speed at to a uniform magnetic field of . It follows a helical path. What is the pitch of the helix? (Proton mass , charge .)

Answer and explanation

Correct answer: B. 0.66 m

  1. Step 1: Resolve the proton velocity into components parallel and perpendicular to the magnetic field: , and .
  2. Step 2: The cyclotron period of the circular motion transverse to the field is .
  3. Step 3: The pitch of the helix is the linear distance traversed along the magnetic field line during one orbital period: .
Answer
0.66 m.
Why not the others: 1.31 m uses the full scalar speed rather than the parallel velocity component ; 1.14 m uses the perpendicular component ; 0.18 m calculates the radius of the helix rather than the pitch.

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