Doubly ionized helium ions are projected with a speed of 10 km s ⁻¹ perpendicular to a uniform magnetic field of magnitude 1.0 T . Calculate the time taken by an ion to complete the circle.

Step-by-step solution

The time period of a charged particle moving in a circular path in a uniform magnetic field is independent of its speed and is given by: T = 2 m qB For a doubly ionized helium ion (alpha particle): Mass, m 4 1.67 10⁻²⁷ kg Charge, q = 2e = 2 1.6 10⁻¹⁹ C Substituting the given values B = 1.0 T and = 3.14 : T = 2 3.14 4 1.67 10⁻²⁷ 2 1.6 10⁻¹⁹ 1.0 T = 3.14 4 1.67 1.6 10⁻⁸ s T 1.31 10⁻⁷ s