A circular coil of radius 10 cm carries a steady current of 10 A . A proton is projected from the center of the coil with a speed of 5 10⁶ m s ⁻¹ in the plane of the coil, as shown in the figure. What is the magnitude of the magnetic force experienced by the proton at the instant it is projected? (Given: charge of proton e = 1.6 10⁻¹⁹ C )

Step-by-step solution

The magnetic field at the center of a circular coil is given by: B = ₀ I 2R Substituting the given values ( I = 10 A , R = 10 cm = 0.1 m ): B = 4 10⁻⁷ 10 2 0.1 = 40 10⁻⁷ 0.2 = 2 10⁻⁵ T The direction of this magnetic field is perpendicular to the plane of the coil. Since the proton is projected in the plane of the coil, the angle between its velocity vector v and the magnetic field B is 90^ . The magnitude of the magnetic force experienced by the proton is: F = qvB Substituting q = 1.6 10⁻¹⁹ C , v = 5 10^6 m s ⁻¹ ,