A partice with a charge of 5 mu C travels in magnetic field

A partice with a charge of 5 mu C travels in magnetic field with a magnitude of 5T. The partice travels in the x-direction at 5 m/s, and maintains a fixed distance above the ground. The partice is in earth\'s gravitational field, subject to a gravitational force (in the -y direction). Draw or explain the direction of the magnetic field on the picture below. What is the force due to the magnetic field? What is the mass of the particle?

Solution

A charged particle moving in presence of a magnetic field suffers a force given as: F = qV x B where the direction of the force is along the cross product of the velocity and the magnetic field.

Part a.) As the particle maintains its direction of motion along the x-direction despite a gravitational force acting on it downwards, the magnetic field must have been balancing the gravitational attraction. That is, the magnetic field must be along the +y axis or upwards in the figure drawn.

Not we know that the direction of the magnetic field is along the cross product of velocity and the magnetic field. Therefore for the magnetic field must be along the - Z axis that is, going into the page for the figure shown.

Part b.) Force due to the magnetic field would be: F = qV x B = 5 x 10^-6 x 5 x 5 = 125 N

Part c.) Now the force due the magnetic field must be balanced by the weight.

That is , Mg = 125 x 10^-6

or, M = 12.742 x 10^-6 kg [using g = 9.81 m/s²]

Therefore the required mass of the particle is 12.742 x 10^-6 kg