Requested Solutions, Homework 12

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The speeds given in the table are either less than or greater than E/B.

Which particles will move out of the page toward you after the instant shown in the figure?

  1. Particles 7, 8, 9, and 10 have velocities that are either parallel or antiparallel to the magnetic field B, and therefore feel no magnetic force, only electric force F=qE (for which the speed is irrelevant).  Particles 7 and 8 are positive, so the force on them is in the same direction as E, into the page.  Particles 9 and 10, with negative charge, move out of the page, in the direction opposite the electric field.
  2. Particles 1, 3, and 5 are moving perpendicular to the magnetic field, so they do feel a magnetic force F=qv×B.  But because their speed is below E/B, the magnitude of the magnetic force qvB is less than the magnitude of the electric force.  Thus whether they move out of the page is determined by the electric force, regardless of whether the magnetic force helps or hinders that.  As in item (1), we only need to look at the sign of the particle.  Particle 5 is negative, and will move out of the page, while 1 and 3 are positive and will move into the page.
  3. Particles 2, 4, and 6 have speeds greater than E/B, and their motion is dominated by the magnetic force (regardless of whether the electric force helps or hinders that).  The cross product v×B has the following directions: 2: out, 4: in, and 6: in. However, the negative charge on particle 6 makes its magnetic force point opposite the cross product, so that 2 and 6 move out of the page, while 4 moves into the page.
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