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 0.90 t. find the time for the proton to make one complete circular orbit.

Time taken by proton to complete one complete circular orbit = 7.28 x 10⁻⁸ s

Explanation:

For proton, the centripetal force required for circular motion is provided by the magnetic force,

so Fm = Fc

q v B = m v²/r

m = mass of charged particle

v = velocity

B = magnetic field

q = charge

r = radius of circular path

v = q B r/m

now v = r ω

ω = angular velocity

ω r = q B r / m

ω=q B / m

now ω = 2π/T where T = time period

so 2π/T=q B/m

T = 2 πm/q B

T = 2π (1.67 x 10⁻²⁷) / [ (1.6 x 10⁻¹⁹) * (0.9) ]

T = 7.28 x 10⁻⁸ s