A particle carrying a charge equal to 1000 times the charge on an electron, is rotating one rotation per second in a circular path of radius ' r ' m . If the magnetic field produced at the centre of the path is x times the permeability of vacuum, the radius ' r ' in m is [ e =1.6 10⁻¹⁹ C ] [ x =2 10⁻¹⁶ ]

Step-by-step solution

Finding the radius of a charged particle's circular path The magnetic field at the center of a circular loop carrying current I with radius r is given by B = ₀ I 2r . A charge Q = 1000e = 1.6 10⁻¹⁶ C rotating with frequency f = 1 Hz produces an effective current I = Qf = 1.6 10⁻¹⁶ A. Given B = x ₀ where x = 2 10⁻¹⁶ , substitution yields x ₀ = ₀ I 2r . Canceling ₀ and solving for r gives r = I 2x = 1.6 10⁻¹⁶ 2 (2 10⁻¹⁶) = 1.6 4 = 0.4 m. The radius is therefore 0.4 m, corresponding to answer choice D.