Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Open-Response Homework Problem 16.2 A particle of unknown mass orbits in the Ear

ID: 1352144 • Letter: O

Question

Open-Response Homework Problem 16.2 A particle of unknown mass orbits in the Earth's magnetic field as shown below. Over the particle's orbit the Earth's field is uniform and the strength of the Earth's field is B = 4 x 10^-5T. The magnetic field is perpendicular to the velocity of the particle. The particle's trajectory is drawn below with the magnetic field directed into the page. The charge of the particle has magnitude |q| = 1.6 x 10^-19C. The radius of the orbit is 4.27m. The particle orbits in the direction drawn with velocity 1/10th the speed of light or 3 x 10^7 m/s. What is the sign of the particle's charge? Justify. (b)What it the mass of the particle? (c) What is the force (magnitude and direction) on the particle at point P? (d) Identify the particle, that is report the name of an elementary particle with features consistent your calculated features of the particle.

Explanation / Answer

(a) The sign of particle's charge is negative , since the trajectory of particle is drawn below with the magnetic field directed into the page.

-----------------------------------------------------------------------------------------------------------------------------------

(b)

Force experieced by the particle in the field

F =qvB

Centripetal force expericed as it move in circular path     

   F = mv2 / r

Equate the two forces ( as long as it moves in that path, both forces are equal )

qvB =mv2 / r

Rearrange for mass of the particle

m = r.q.B / v

Substitute given values

m = ( 4.27 ) (1.6 x 10-19 C ) ( 4 x 10 -5 ) / 3 x 107

m = 9.1 x 10-31 kg

---------------------------------------------------------------------------------------------------

(c)

Force on the particle:

F = qvB

= (1.6 x 10-19 C ) (3 x 107)( 4 x 10 -5 )

= 1.9 x 10-16 N

The direction foce is upward

----------------------------------------------------------------------------------------------------

(d)

From the above results, it is clear that the particle is electron