A particle of mass 1 10⁻²⁷ ~kg and charge 1 10⁻¹⁶ C enters the uniform magnetic field within the solenoid, at speed 1000 ~ms ⁻¹ . The velocity vector makcs an angle 60^ with the axis of solenoid. The solenoid has 5000 turns along its length and carries current 5 ~A . The number of revolution the particle makes along the helical path within the solenoid by the time it emerges from solenoid's opposite end is

Step-by-step solution

The given situation is shown below. Given, aligned v & =1000 ~m / s q & =10⁻¹⁶ C m & =1 10⁻²⁷ ~kg aligned aligned N & = Number of turns =5000 I & =5 ~A R & = Radius of circular path of charge aligned R= Radius of circular path of charge Magnetic field, B= ₀ n l (where, n= number of turns per unit length) aligned & B= ₀ N L I (where, n= N L ) & B= ₀ 5000 L 5 & B= ₀ 25000 L ...(i) aligned Also we know that, Distance = speed time L=v_x t (where, v_x is the component of velocity along the axis of the solenoid) L=500 t.