The uniform 28.0 mT magnetic field in the figure points in the positive z direct
ID: 777018 • Letter: T
Question
The uniform 28.0 mT magnetic field in the figure points in the positive z direction. An electron enters the region of magnetic field with a speed of 5.50 × 106 m/s and at an angle of 30° above the xy-plane. (Figure 1) Part A Find the radius r of the electron's spiral trajectory Express your answer with the appropriate units alueUnits Submit Request Answer Part B Find the pitch p of the electron's spiral trajectory Express your answer with the appropriate units alue Units Submit Request Answer gure 1 of 1 Provide Feedback 30°Explanation / Answer
(A) magnetic force is
FM=qv x B = qvBsin(/2-) = qvBcos
this force equals the centripetal force
FC=mv^2cos^2/r
then
mv^2cos^2/r=qvBcos
the radius of the spiral is
r=mvcos/(qB)
= (9.11*10-31)(5.5*106)cos30/(1.6*10-19 * 28*10-3)
= 9.69 x 10-4 m
(B)
the pitch is
p=vsinT
where
T=2r/(vcos)
then
p=2rtan
= 2*9.69 x 10-4 *tan30
= 3.51 x 10-3 m
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