I. A uniform magnetic field, B 20mT2 acts on a -5.OnC charge with mass 1.0g trav

Question

I. A uniform magnetic field, B 20mT2 acts on a -5.OnC charge with mass 1.0g travelling with velocity v (-2,2,1)m/s a) What is the component of the velocity in the direction parallel to the magnetic field? b) What is the component of the velocity perpendicular to the magnetic field? c) Calculate the radius r of the trajectory. d) The electron will travel in a spiral (also called a helix). Why? What is the direction of axis of the spiral? How far along the axis will the electron progress in the time it takes to make one loop of the spiral? (In other words, what is the 2R pitch, p, of the spiral?) Time

Explanation / Answer

given,

magnetic field = -20 * 10^-3 T

charge = -5 * 10^-9 C

velocity = (-2, 2, 1) m/s

since the magnetic field is in z axis so conponent of velocity in z axis or magnetic field is 1 m/s

perpendicular to magnetic field is perpendicular to z axis that is x and y axis

so resultant of x and y axis = sqrt((-2)^2 + 2^2)

so resultant of x and y axis = sqrt((-2)^2 + 2^2)

component of velocity perpendicular to the magnetic field = 2.828 m/s

radius = mass * perpenducular velocity / charge * magnetic field

radius = 1 * 10^-3 * 2.828 / (5 * 10^-9 * 20* 10^-3)

radius = 28280000 m

direction of the axis of the spiral is z axis

pitch = time period * parallel velocity

pitch = 2 * pi * m / Bq * 1

pitch = 2 * pi * 1 * 10^-3 / (20 * 10^-3 * 5 * 10^-9) * 1

pitch = 6.28 * 10^7 m

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