Assume the region to the right of a certain plane contains a uniform magnetic fi
ID: 2273534 • Letter: A
Question
Assume the region to the right of a certain plane contains a uniform magnetic field of magnitude b = 1.63 mT and the field is zero in the region to the left of the plane as shown in the figure below. An electron, originally traveling perpendicular to the boundary plane, passes into the region of the field.
Assume the region to the right of a certain plane contains a uniform magnetic field of magnitude b = 1.63 mT and the field is zero in the region to the left of the plane as shown in the figure below. An electron, originally traveling perpendicular to the boundary plane, passes into the region of the field. Determine the time interval required for the electron to leave the "field-filled" region, noting that the electron's path is a semicircle. Assuming the maximum depth of penetration into the field is 2.67 cm, find the kinetic energy of the electron.Explanation / Answer
a)
Lorentz force =Centripetal force
qVB =mV^2/r
qB =m(V/r )
since W=V/r
qB =mW
and W=2pi/T
qB=2pim/T
T=2pim/qB
which is cyclotron frequency
we want
dT =T/2 =pim/qB
dT =pi*9.11*10^-13/(1.6*10^-19)*(1.63*10^-3)
dT=1.097*10^-8 s =1.1*10^-8 s
b)
KE=(1/2)mV^2
V=Wr =(qB/m)
KE=(1/2)(q^2*B^2*r^2/m)
KE=(1/2)(1.6*10^-19)^2*(1.63*10^-3)^2*0.0267^2/(9.11*10^-31)
KE=2.66*10^-17 J
KE =2.66*10^-17/1.6*10^-19
KE=166.33 eV