Section 3 review
When a charged particle moves within a magnetic field, it feels a force. The force vector is perpendicular to the magnetic field and to the particle’s velocity vector; this means that the force often causes charged particles to follow curved paths. The strength of the force is proportional to the magnetic field strength, the particle’s charge, and the particle’s speed. This force has many practical applications because it can separate particles with differing masses or electrical charges. Read the text aloud
mass spectrometer, cyclotron radius, permeability of free space, voice coil, galvanometer, cathode ray tube (CRT)

F B =qvBsinθ
m= rqB v
B= μ 0 I 2πr

Review problems and questions

What is the sign of the particle charge in each case?
  1. As shown here, the right-hand rule tells us the direction of the force on a positively charged particle that moves with velocity v through a magnetic field B. The first magnetic spectrometer shows the trajectories of positively charged particles entering from the left. What is the sign (+ or −) of the particle charge in Case (a) and Case (b)? The magnetic field emerges from the page toward the viewer in all three spectrometers. Read the text aloud Show
  1. In each spectrometer shown on this page, three charged particles enter with identical velocities, but soon they follow different paths. Which of the following could explain why their paths diverge? (Recall that each of the three particles is in the same magnetic field.)
    1. The particles have differing masses.
    2. The particles have differing amounts of electric charge.
    3. Either a or b.
    4. Neither a nor b. Read the text aloud Show
Calculate the strength of the electromagnetic force
  1. Calculate the strength of the electromagnetic force upon the positive charge in each of these three cases. (Note that the force will point toward you, at right angles to the page, since the charge is positive and the magnetic field and velocity vectors both lie in the plane of the page.) The field strength, speed, and charge remain constant; only the angle between the two vectors is varied. Read the text aloud Show

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