A particle of mass 2.2 10⁻³⁰ ~kg and charge 1.6 10⁻¹⁹ C is moving at a speed of 10 ~km ~s ⁻¹ in a circular path of radius 2.8 ~cm inside a solenoid. The solenoid has 25 turns cm and its magnetic field is perpendicular to the plane of the particle's path. The current in the solenoid is ( . Take, ₀=4 10⁻⁷ Hm ⁻¹ )

Step-by-step solution

Given, mass of the particle, m=22 10⁻³⁰ ~kg Charge, q=1.6 10⁻¹⁹ C Velocity, v=10 kms ⁻¹=10^4 ~ms ⁻¹ Radius of circular path, r=2.8 ~cm =2.8 10⁻² ~m n=25 turns / cm =2500 turns m Since, r=m v / B q ...(i) Magnetic field inside the solenoid, B= ₀ n I ...(ii) From Eqs. (i) and (ii), we get r= m v ( ₀ n I ) q I= m v ₀ n q r aligned & = 2.2 10⁻³⁰ 10^4 4 10⁻⁷ 2500 1.6 10⁻¹⁹ 2.8 10⁻² & =1.56 10⁻³ ~A =1.56 ~mA aligned