G Three particles of equal charge, X, Y, and Z, enter a uniform magnetic field B. X has velocity of magnitude v parallel to the field. Y has velocity of magnitude v perpendicular to the field. Z has equal velocity components v parallel and perpendicular to the field. Rank the radii of their orbits from least to greatest.

or radius of  Y< rad of Z< radius of X.

Explanation:

For a particle moving in a circular orbit in a magnetic field, the centripetal force must equal the magnetic force:

where the magnetic force has the magnitude

;

therefore,

Now, for the particle X, since it is parallel to the magnetic field; therefore, it will experience no force and .

For the particle, Y , and therefore, it will experience the greatest force, and thus its orbit will be the tightest (the radius will be the smallest)

Finally, for the particle Z, because its velocity will have both parallel and perpendicular components; therefore, the radius of its orbit will be greater than for particle Y, but less than for particle X.

Thus the radii, when ordered from least from greatest are

.