Question

A uniform magnetic field of magnitude 0.20 T exists in space from east to west. With what speed should a particle of mass 0.010 g and with charge 1.0 × 10⁻⁵ C be projected from south to north so that it moves with uniform velocity?

Answer 1

Given:
Uniform magnetic field, B = 0.20 T
Mass of the particle, m = 0.010 g = 1 × 10⁻⁵ kg
Charge of the particle, q = 1.0 × 10⁻⁵ C
As per the question, if the particle has to move with uniform velocity in the region of the applied field,
gravitational force experienced by the particle should be equal to the magnetic force experienced by the particle.
So, qvB = mg, where v is the uniform velocity and g is the acceleration due to gravity.
⇒ 1 × 10⁻⁵ × v × 2 × 10⁻¹ = 1 × 10⁻⁵ × 9.8
⇒ v = 4.9 × 10 = 49 m/s