A uniform magnetic field of magnitude 0.20 T is directed from east to west in space. At what speed must a particle of mass 0.010 g and charge 1.0 10⁻⁵ C be projected from south to north in order to travel with a uniform velocity?

Step-by-step solution

Let the directions be represented by unit vectors: East as i , North as j , and vertically upward as k . The magnetic field is directed from East to West, so B = -B i . The particle is projected from South to North, so its velocity is v = v j . The magnetic force on the particle is F _m = q( v B ) = q(v j (-B i )) = qvB k . The magnetic force acts vertically upwards. For the particle to travel with uniform velocity, the net force must be zero. Thus, the upward magnetic force must balance the downward gravitational