An alpha particle is moving with a speed of 10^5 m/s parallel to a long straight current-carrying conductor. The perpendicular distance between the alpha particle and the conductor is 10 cm . If the alpha particle experiences a magnetic force of 6.4 10⁻¹⁹ N , calculate the current flowing in the conductor.

Step-by-step solution

The magnetic force on a moving charge is given by F = qvB . For an alpha particle, the charge is q = +2e = 2 1.6 10⁻¹⁹ C = 3.2 10⁻¹⁹ C . Since the particle moves parallel to the straight wire, its velocity is perpendicular to the circular magnetic field lines produced by the wire ( = 90^ ). The magnetic field B at the position of the alpha particle is: B = F qv = 6.4 10⁻¹⁹ 3.2 10⁻¹⁹ 10^5 = 2 10⁻⁵ T . The magnetic field due to a long straight wire is B = ₀ I 2 r . Rearranging for the current I and substituting r = 1