Particle enters a magnetic field. Question 2.

Question – Source: Yahoo! Answers !

A proton, mass 1.67 · 10 -27 kg and charge +1.6 · 10 -19 C, moves in a circular orbit perpendicular to a uniform magnetic field of 0.82 T.
Find the time for the proton to make one complete circular orbit.

Solution.

The Newton’s Second Law : F=m*a

Circular motion formulas:
a= v^2/r ; v=2*pi*r/T

Electromagnetic force on the proton (Lorentz Force) :
F=q*v*B*sin(a);
sin(a) = 1 because circular orbit perpendicular to a uniform magnetic field ;

So,

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

q*B=m*v/r

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

T=2*pi*m/(q*B) ; the time for the proton to make one complete circular orbit;

T= 2*3.14*1.67*10^-27/(1.6*10^-19*0.82) = 8*10^-8 s

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