The variable quantity when a charged particle moves at right angles to the magnetic field is momentum. This is because the magnetic force acting on the particle causes it to change direction, but not speed. Therefore, the particle's momentum changes due to the change in direction.

Explanation:

Magnetic force is given by the equation F = q(v x B), where F is the force, q is the charge of the particle, v is the velocity of the particle, and B is the magnetic field. When the particle moves at right angles to the magnetic field, the velocity vector v is perpendicular to the magnetic field vector B. This means that the cross product v x B is a vector perpendicular to both v and B, and its magnitude is equal to the product of the magnitudes of v and B multiplied by the sine of the angle between them. Therefore, the magnetic force is perpendicular to both v and B, and its magnitude is given by F = qvBsin(theta), where theta is the angle between v and B.

Since the magnetic force is perpendicular to the velocity of the particle, it does not change the speed of the particle. However, it does change the direction of the particle's motion, causing it to move in a circular path. This means that the particle's momentum changes due to the change in direction. The momentum vector is given by p = mv, where m is the mass of the particle. Since the velocity vector changes direction, the momentum vector also changes direction, but not magnitude. Therefore, the variable quantity when a charged particle moves at right angles to the magnetic field is momentum.