Question

A particle of mass m and charge q is accelerated from rest in the plane of the page through a potential difference V between two parallel plates as shown. The particle is injected through a hole in the right-hand plate into a region of space containing a uniform magnetic field of magnitude B oriented perpendicular to the plane of the page. The particle curves in a semicircular path and strikes a detector.

a. i. State whether the sign of the charge on the particle is positive or negative.

ii. State whether the direction of the magnetic field is into the page or out of the page.

b. Determine each of the following in terms of m, q, V, and B.

i. The speed of the charged particle as it enters the region of the magnetic field B

ii. The force exerted on the charged particle by the magnetic field B

iii. The distance from the point of injection to the detector

iv. The work done by the magnetic field on the charged particle during the semicircular trip

Answer 1

(a) i) since the particle is accelerated toward the negatively charged plate, it must be positively charged

ii) The force on the particle due to the magnetic field is towards the center of the circular arc. By RHR the magnetic field must point out of the page.

(b) i) W = K … Vq = ½ mv² … v = √ (2Vq/m)

ii) F_b = qvB = qB (√ (2Vq/m) )

iii) F_net(C) = mv²/r … qvB = mv² / r … r = mv / Bq … distance is 2xr = 2mv/qB

iv) Work traveled in a circle at constant speed is zero as described in previous units.