A uniform magnetic field, directed perpendicular to the page, is confined to the

Question

A uniform magnetic field, directed perpendicular to the page, is confined to the large square region in the figure at right. The figure shows the paths taken by four particles through this region.

(a) Using the information given in the diagram, complete the table below listing the various parameters for the different particles. Each particle takes a different path through the field. Determine which particle took which path, and find the mass of particle 4.

A uniform magnetic field, directed perpendicular to the page, is confined to the large square region in the figure at right. The figure shows the paths taken by four particles through this region. (a) Using the information given in the diagram, complete the table below listing the various parameters for the different particles. Each particle takes a different path through the field. Determine which particle took which path, and find the mass of particle 4.

Explanation / Answer

Particle 1 takes path C. Since there is no charge, there is no force to change its direction

For the rest...

Apply r = mv/qB

For particle 2... r = (2m)(2v)/(2q)(B) ... By the numbers , 2(2)/2 = 2

For particle 3... r = (4m)(v)/(q)(B)... By the numbers, 4(1)/(1) = 4

For particle 4... r = (?)(2v)/qB

What we can see, then, is that particle 3 must take the path with the big radius. Since 4 is bigger than two. Also since we have two small radii, we have to have particles 2 and 4 taking those small paths...

Thus particle 3 takes path D

Particle 2 must take path A. The reason it is positive like particle 3, so it must move in the same direction circle. Both are clockwise.

That leaves path B for particle 4.

Also, since the numbers for particle 4 must be 2, the mass must be 1m.

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