Problem 29.22a Serway and Jewett Assume the region to the right of a certain pla

Question

Problem 29.22a Serway and Jewett Assume the region to the right of a certain plane contains a uniform magnetic field, B, of magnitude 3.37 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. Determine the time interval required for the electron to leave the "field-filled" region, noting that the electron's path is a semicircle ? 0 Figure P29.22 (b) Assuming the maximum depth of penetration into the field is 3.0 cm, find the kinetic energy of the electron

Explanation / Answer

a) F = q v B sin theta

F = m a

q v B sin theta = m a

q v B sin theta = m (v2 / r)

r = m v / q B

T = 2 pi / v * (m v / q B)

T = 2 pi m / q B

= (2 pi * 9.11 * 10-31 ) / (1.6 * 10-19 * 3.37 * 10-3) = 1.06 * 10-8 s

delta t = T/2

time interval rquired = 0.53 * 10-8 s

b) KE = 1/2 m v2 = 1/2 m (q B r / m)2

= q2 B2 r2 / 2 m

= ((1.6 * 10-19)2 * (3.37 * 10-3)2 * 0.032) / (2 * 9.11 * 10-31)

= 1.44 * 10-16 J

= 898 eV

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