Assume the region to the right of certain plane contains a uniform magnetic fiel

Question

Assume the region to the right of certain plane contains a uniform magnetic field of magnitude B = 1 mT and the field is zero in the region to the left of the plane as shown in the figure. An electron, originally travelling perpendicular to the boundary plane, passes into the region of the field. Determine the time interval required for electron to leave the "field-filled" region, noting that the electron's path is a semicircle. Assume the maximum depth of penetration into the field is 2 cm, find the kinetic energy of the electron As the electron enters the field, in what direction (up, down, into the page, out of page) will be deflected?

Explanation / Answer

given

B = 1 mT

B = 1 X 10-3 T

a )

using equation for T is

T = 2 m / q B

T = 2 X 3.14 X 9.1 X 10-31 / 1.6 X 10-19 X 1 X 10-3  

T = 3.57 X 10-8 sec

change in time is dt = T / 2

dt = 3.57 X 10-8 / 2

dt = 1.78 X 10-8 sec

b )

given r = 2 cm = 0.02 m

the KE = 1/2 m v2 -- 1

but we know r = mv / qB

v = q B r / m

v value substituting in equation 1

KE = 0.5 X m X ( qB r / m )2

KE = 0.5 X 1.62 X 10-38 X 10-6 X 0.022 / 9.1 X 10-31

KE = 5.626 X 10-18 J

KE = 5.626 X 10-18 / 1.6 X 10-19

KE = 35.16 eV

c )

into the page

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