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

Question

Assume the region to the right of a certain plane contains a uniform magnetic field of magnitude b = 1.77 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. B=O B=b (a) Determine the time interval required for the electron to leave the ?field-filled? region, noting that the electron?s path is a semicircle. s (b) Assuming the maximum depth of penetration into the field is 3.20 cm, find the kinetic energy of the electron. eV

Explanation / Answer

F= BeV

we F = ma

so

a = Bev/m where e is the lectron charge

time taken to pentrate through the field length of d is

d= 0.5 at^2

t= 2d/a where a si the acceleration given by the above equation

ii) if it pentrates through a length of d= 3.2 cm the velocity is

velocity v = qBr/m = 1.77*10^-3*3.2*10^-3*1.71*10^11 = 9.6*10^5 m/sec

so kinetic energy = 0.5mv^2 = 0.5*9.1*10^-31* 9.2*10^12 =26.41 ev

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