Planar Motion An electron enters a magnetic field of 0.35 T, moving perpendicula
ID: 1359793 • Letter: P
Question
Planar Motion
An electron enters a magnetic field of 0.35 T, moving perpendicular to it with a speed of 3·105 m/s.
a) Find the radius of the orbit that it will make.
b) If the magnetic field points directly away from you (into the page), then this orbit would be in which direction from your perspective?
Helical Motion
If an electron were sent at the same speed, but at an angle of 70o to the magnetic field:
a) What would be the radius of the helical motion?
b) How long would it take for the electron to travel 3 m along ("downstream" to) the magnetic field?
Explanation / Answer
B =0.35 T, v = 3x105 m/s
mass of electron m =9.1x10^-31 kg, e =1.6x10^-19 C
In circular motion F =mv2/r
F =qvBsin(90)
mv2/r = qvBsin(90)
r = mv/qB
r = (9.1x10-31)(3x105)/(1.6x10-19)(0.35)
r =4.82x10-6 m
(b)
(a) theta =700
r =mv/qBsin(70)
r =4.82x10-6 /sin(70)
r =5.13x10-6 m
(b) s=3 m,
a =v2/r = (3x105)2/(5.13x10-6)
a = 1.75x1016 m/s2
s =ut+(1/2)at2
3 =(3x105)t+(1/2)(1.75x1016 )t2
(1.75x1016 )t2 +(6x105)t -6 =0
By solving abive equation we get
t = 1.85x10-8 s