An electron enters a region of space where there is a magnetic field B = 7 mT k with a velocity v = (9 × 10^6m?
/s)i + (7 × 10^6m/s) j + (5 × 10^6 m/s) k . What is the spacing of the circles of the helix on which the electron moves?
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F = qv x B (F, v, and B are vectors)
For the components of v perpendicular to B (vp in xy-plane),
m(vp)²/r = q(vp)B
(vp)/r = qB/m
ωp = qB/m
ωp = (-1.6e-19 C)(7e-3 T) / (9.1e-31 kg)
ωp = 1.23e9 rad/s
T = 2π/(ωp)
T = 2π / (1.23e9 rad/s)
T = 5.1e-9 s
Spacing between circles of helix would be the change in z for one period.
(5e6 m/s)(5.1e-9 s) = 2.6e-2 m or 2.6 cm
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