Which of the subsequent conditions must be met in order for a uniform magnetic field to exert a force on a particle?

Ans:

A charged particle has to be in a magnetic ground in order for that magnetic field to exert a force on the charged particle. That is why it makes no wisdom to say that a magnetic field attracts or repels a charged particle.

A consistent magnetic field exerts no force on an uncharged particle in that magnetic field. Specified a charged particle in a magnetic field the charged particle has to be crossing some magnetic field lines in order for the magnetic field to exert a force on it. The charged particle isn't crossing magnetic field lines if it is at rest or if it is moving along a magnetic field line or in the exact opposite direction to that of the magnetic field line it is on.

The mathematical appearance for the force exerted on a charged particle by a magnetic field must of course be consistent with the conceptual statements above. Certainly the expression

for the force exerted through a charged particle by a magnetic field yields a force whose magnitude is given by

F = qvBsinq

This is a result of four multiplicands. If every one of the multiplicands is zero the force F exerted by the magnetic field on the particle in question is as well zero. Specifically if the charge q is zero the speed of the particle v is zero the magnetic field B is zero (as it is outside the region where the magnetic field exists) or the sine of the angle in between the velocity of the particle and the direction of the magnetic field is zero as it is when θ is 0° or 180° corresponding to the velocity being parallel or anti parallel to the magnetic field respectively) then the force exerted by the magnetic field on the particle is zero.