29 P Assume the region to the right of a certain plane contains a uniform magnet

Question

29 P Assume the region to the right of a certain plane contains a uniform magnetic field of magnitude b-1.73 mT and the field is zero in the region to the left of the plane as shown in the figure to the boundary plane, passes into the region of the field vXxXXX (e) Determine the time interval required for the electron to leave the "field-filled" region, noting that the electron's path is a semicircle. (b) Assuming the maximum depth of penetration into the field is 2.45 cm, find the kinetic energy of the electron.

Explanation / Answer

here,

magnitude of magnetic feild , B = 1.73 mT = 0.00173 T

a)

the time taken to complete semicircle , t = (2 * pi * m /( q * B)) /2

t = ( pi * m )/(q * B)

t = (pi * 9.1 * 10^-31 )/( 1.6 * 10^-19 * 0.00173 )

t = 1.03 * 10^-8 s

b)

the maximum penetration , r = 2.45 cm = 0.0245 m

r = m * v /( q * B)

0.0245 = 9.1 * 10^-31 * v / ( 1.6 * 10^-19 * 0.00173)

solving for v

v = 7.45 * 10^6 m/s

the kinetic energy , KE = 0.5 * m * v^2 /q eV

KE = 0.5 * 9.1 * 10^-31 * (7.45 * 10^6)^2 /( 1.6 * 10^-19) eV

KE = 157.8 eV

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