Question

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.

Answer 1

`R_Y<R_Z<R_X` or radius of Y< rad of Z< radius of X.

Step-by-step explanation:

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

`(mv^2)/(R) = F_B`

where the magnetic force
`F_B` has the magnitude

`F_B =qvBsin(\theta)`;

therefore,

`(mv^2)/(R) = qvBsin(\theta)`

`R= (mv)/(qBsin(\theta)).`

Now, for the particle X,
`\theta =0` since it is parallel to the magnetic field; therefore, it will experience no force and
`R = \infty`.

For the particle, Y
`\theta = 90^o`, 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,
`0<\theta<90^o` 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

`R_Y<R_Z<R_X`.