Assume the region to the right of a certain plane contains a uniform magnetic fi
ID: 2121714 • Letter: A
Question
Assume the region to the right of a certain plane contains
a uniform magnetic field of magnitude 1.00 mT and the
field is zero in the region to the left of the plane as shown
in Figure P29.22. An electron, originally traveling perpendicular
to the boundary plane, passes into the region of
the field. (a) Determine the time interval required for the
electron to leave the %u201Cfield-filled%u201D region, noting that the
electron%u2019s path is a semicircle. (b) Assuming the maximum
depth of penetration into the field is 2.0 cm, find the kinetic energy of the electron.
Explanation / Answer
a) time would be period/2
we know q vB = mv^2/r
v = q B r/m
v = 2 pi r /T
2 pi r/T = q B r/m
2 pi/T = q B/m
T/(2 pi ) = m/(qB)
T/2 = 9.11E-31*pi/(1.6E-19*1.0E-3)=1.79E-8 s
b) this means r= 2 cm
v = q B r/m = 1.6E-19*1.0E-3*2.0E-2/(9.11E-31)=3.51E6
so KE = 0.5*9.11E-31*3.51E6^2=5.61E-18 J