A positive charge q is projected in magnetic field of width m v 2 q B with velocity v . Then, the time taken by charged particle to emerge from the magnetic field is

Step-by-step solution

Referring the diagram, width of magnetic field w = m v 2 q B Also we know that when a charge is projected in perpendicular magnetic field then radius of path is R = m v q B Now in triangle OAB, sin θ = w R = m v 2 q B m v q B = 1 2 ⇒   sin θ = sin 45 ° = sin π 4 Time period for angle 2 π is T = 2 π m q B ∴ Time by charged particle for θ = π 4 in order to emerge from magnetic field is T = π m 4 q B .