A particle travels in a circle of diameter 1.0 cm under the influence of a 0.40 T magnetic field. The application of a 200 V m ⁻¹ electric field makes the path straight. Determine the charge-to-mass ratio of the particle.

Step-by-step solution

When the path of the particle is straight under the combined electric and magnetic fields, the electric force balances the magnetic force. qE = qvB v = E B Substituting the given values E = 200 V m ⁻¹ and B = 0.40 T : v = 200 0.40 = 500 m s ⁻¹ When the particle travels in a circle under the influence of the magnetic field alone, the radius of the circular path is given by: r = mv qB Rearranging for the charge-to-mass ratio: q m = v rB The diameter of the circle is 1.0 cm , so the radius is r = 0.5 cm = 5 10⁻³ m . S