A positive particle of mass m and charge q moves in uniform parallel fields B=Bk̂ and E=Ek̂. At t=0 its velocity is v⊥î+v∥k̂. What is the pitch of the helix during the nth complete revolution, measured as the axial displacement between the starts of the nth and (n+1)th revolutions?
Options

Question

A positive particle of mass m and charge q moves in uniform parallel fields B=Bk̂ and E=Ek̂. At t=0 its velocity is v⊥î+v∥k̂. What is the pitch of the helix during the nth complete revolution, measured as the axial displacement between the starts of the nth and (n+1)th revolutions?

Options

G1 Physics · Accepted Answer

The axial coordinate is z=v∥t+(qE/2m)t². The nth pitch is z((n+1)T)−z(nT)=v∥T+(qE/2m)(2n+1)T², where T=2πm/(qB).