A particle of charge 2.0 × 10−8 C and mass 2.0 × 10−10 g is projected with a speed of 2.0 × 103 m s−1 in a region with 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.
Charge of the particle, q = 2.0 × 10−8 C
Mass of the particle, m = 2.0 × 10−10 g
Projected speed of the particle, v = 2.0 × 103 m s−1
Uniform magnetic field, B = 0.10 T.
As per the question, the velocity is perpendicular to the field.
So, for the particle to move in a circle,the centrifugal force to the particle will be provided by the magnetic force acting on it.
Using qvB =`(mv^2)/(r)` , where r is the radius of the circle formed,
`r = (mv)/(qB)`
= 20 cm
`T = (2pim)/(qB)`
= 6.28 × 10-4 s