Question

A positron with kinetic energy 1.60 keV is projected into a uniform magnetic field of magnitude 0.140 T, with its velocity vector making an angle of 83.0° with the field. Find (a) the period, (b) the pitch p, and (c) the radius r of its helical path.

Answer 1

1ev = 1.6*10^-19 J

mass of positron = 9.11*10^-31 kg

kinetic enenrgy K = (1/2)*m*v^2 = 1.6*10^3*1.6*10^-19 J

(1/2)*9.11*10^-31*v^2 = 1.6*10^3*1.6*10^-19

speed of positron v = 2.37*10^7 m/s

Fnet = m*a

Fnet = magnetic force = q*v*B*sintheta

acceleration a = (v*sintheta)^2/r

q*v*B*sintheta = m*(v*sintheta)^2/r

radisu r = m*v*sintheta/(q*B)

time period T = 2*pi*r/(v*sintheta)

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

T = 2*pi*9.11*10^-31/(1.6*10^-19*0.14)

T = 2.56*10^-10 s <<<-----------answer

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part(b)

pitch p = vh*T = v*costheta*T

p = 2.37*10^7*cos83*2.56*10^-10 = = 7.4*10^-4 m = 0.74 mm <<<---answer

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part(c)

radius r = m*v*sintheta/(q*B)

r = 9.11*10^-31*2.37*10^7*sin83/(1.6*10^-19*0.14)

r = 9.6*10^-4 m