A particle having a charge of 2.0 × 10–8 C and a mass of 2.0 ×10–10 g is projected with a speed of 2.0 × 103 ms–1 in a region having a uniform magnetic field of 0.10 T. The velocity is perpendicular to the field. Find the radius of the circle formed by the particle and also the time period.

Given-



Charge on the particle, q = 2.0 × 10−8 C



Mass of the particle, m = 2.0 × 10−10 g



velocity of the particle when projected, v = 2.0 × 103 m s−1



Magnetic field, B = 0.10 T.



Given in the question that, the velocity is perpendicular to the field.



So, for the particle to move in a circle, the centrifugal force comes into acts which is provided by the magnetic force acting on it.


Also magnetic force, we know, Lorentz force F is given by -



where,


e = charge on an electron


v = velocity of the electron


B=magnetic field



Using the formula for centrifugal force



where,


v= velocity of the particle


r= radius of circle form


m =mass of the electron


Equating the two forces, we will get-






Now,


Time period,





1