A particle of charge 25 pc and mass 1.0 x 10-15 kg moves at a speed of 1795 m/s,

Question

A particle of charge 25 pc and mass 1.0 x 10-15 kg moves at a speed of 1795 m/s, and its velocity vector lies in the xy plane. There is a magnetic field of magnitude 0.86 Talong the +z direction. The magnetic force on the particle causes the particle to move in a circle that lies in the x-y plane. (a) Find the radius of this circle. m (b) Find the period of the motion. (c) If the particle is moving parallel to +y att tro, is the circular motion clockwise or is it counterclockwise as viewed from along the +. Z axis? clockwise counterclockwise

Explanation / Answer

a)
Let the particle is revolving in circle of radius r
Centripetal acceleration = v^2/r
Centripetal force = mv^2/r
Force = qbv

Equating the two we get
mv^2/r = qbv
=> r = mv/qb
=> r = (1.0*10^-15*1795)/(25*10^-6*0.86)
=> r = 8.35*10^-8 m

b) Distance = 2*pi*r
speed = 1795 m/s
time period = distance/speed
= (2*pi*8.35*10^-8) /1795
= 2.9*10^-10 s

c)The circular motion is clockwise as viewed from the positive z-axis

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