The uniform 35.0mT magnetic field in the figure points in the positive z-directi
ID: 1282879 • Letter: T
Question
The uniform 35.0mT magnetic field in the figure points in the positive z-direction. An electron enters the region of magnetic field with a speed of 5.40 X10^6m/s and at an angle of 30* above the xy-plane.
Part A Find the radius r of the electron's spiral trajectory.
Part B Find the pitch p of the electron's spiral trajectory
The uniform 35.0mT magnetic field in the figure points in the positive z-direction. An electron enters the region of magnetic field with a speed of 5.40 X10^6m/s and at an angle of 30* above the xy-plane. Part A Find the radius r of the electron's spiral trajectory. Part B Find the pitch p of the electron's spiral trajectoryExplanation / Answer
a)
component of veloity perpendicular to B,
v = 5.4*10^6*cos(30)
= 4.67*10^6 m/s
we know, m*v^2/r = q*v*B
==> r = m*v/B*q
= 9.1*10^-31*4.67*10^6/(0.035*1.6*10^-19)
= 7.60*10^-4 m
B) Time periode, T = 2*pi*m/(B*q)
= 2*pi*9.1*10^-31/(0.035*1.6*10^-19)
= 1.02*10^-9 s
pitch, p = vz*T
= 5.4*10^6*sin(30)*1.02*10^-9
= 2.754*10^-3 m
= 2.754 mm
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