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A charged particle with charge-to-mass ratio q/m = 5.0 x 10^7 C/kg…
Question
A charged particle with charge-to-mass ratio q/m = 5.0 x 10^7 C/kg moves with velocity having components (3.0 x 10^5, 0, 4.0 x 10^5) m/s in a uniform magnetic field B = (0, 0, 0.20) T. The particle follows a helical path. Find the pitch of the helix (in metres).
✓ Verified answer: 0.251327checked by our engine — not a guess
Step-by-step solution
The field is along z, so the velocity component parallel to B is v_par = 4.0e5 m/s (the z-component); the perpendicular component causes circular motion.
Period T = 2*pi*m/(qB) = 2*pi/((q/m)B) = 2*pi/(5.0e7 x 0.20) = 2*pi/1.0e7 = 6.2832e-7 s.
Pitch = v_par x T = 4.0e5 x 6.2832e-7 = 0.251327 m.
Final answer0.251327
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