An electron and a proton (p\') are injected into a magnetic field at the same SP

Question

An electron and a proton (p') are injected into a magnetic field at the same SPEED, as seen below. The velocity vectors shown are at right angles to the magnetic field X = into page. Draw a qualitative sketch of the paths followed by p^+ and c' on the figure showing direction of travel with an arrow. If the speed of each particle is 5.0 times 10^7 m/s and the magnetic field has magnitude 0.5 T, calculate the force on the electron. Calculate the radius r_e of the electron's path. If the mass of the proton is * 2000 m_what is the approximate radius of the proton's path?

Explanation / Answer

a) the path of proton is clockwise cirlce with greater radius

the path of the electron is counter clockwise circle with smaller radius.

b) Force on electron = q_e*v*B*sin(90)

= 1.6*10^-19*5*10^7*0.5

= 4*10^-12 N

c) Apply, F = q*v*B

m*a = q*v*B

m*v^2/r = q*v*B

==> r = m*v/(B*q)

= 9.1*10^-31*5*10^7/(0.5*1.6*10^-19)

= 5.7*10^-4 m

d) radius of proton = 2000*5.7*10^-4

= 1.14 m

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