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,