An electron travels along a circle of radius 1 m in a perpendicular magnetic field of strength 0.50 T . What would its speed be, and is this speed reasonable?

Step-by-step solution

The radius of the circular path of a charged particle in a perpendicular magnetic field is given by r = mv qB . Rearranging for speed v , we get v = qBr m . Substituting the given values: v = 1.6 10⁻¹⁹ 0.50 1 9.1 10⁻³¹ v = 0.8 10⁻¹⁹ 9.1 10⁻³¹ 8.8 10¹⁰ m s ⁻¹ The calculated speed is 8.8 10¹⁰ m s ⁻¹ , which is significantly greater than the speed of light in vacuum ( c = 3 10⁸ m s ⁻¹ ). Since no material particle can travel faster than the speed of light, this speed is unreasonable.