Particle roundabout. Figure 28-29 shows 11 paths through a region of uniform mag

Question

Particle roundabout. Figure 28-29 shows 11 paths through a region of uniform magnetic field. One path is a straight line;: the rest are half-circles. Table 28-4 gives the masses, charges, and speeds of 11 particles that take these paths through the field in the directions shown. Which path in the figure corresponds to which particle in the table? (The direction of the magnetic field can be determined by means of one of the paths, which is unique.) A charged particle enters a uniform magnetic field B with speed v_0, moves through a half-circle in time T_0, and then leaves the field. (a) Is the charge positive or negative? (b) Is the final speed of the particle greater than, less than, or equal to v_0? (c) If the initial speed had been 0.5v_0, would the time spent in field B have been greater than, less than, or equal to T_0? (d) Would the path have been a half-circle, more than a half-circle, or less than a half-circle?

Explanation / Answer

We know the formula R= (m.v)/(q.B)

As here in the table magnetic field(B) is not given , so it is same for all particle.

Using the above formula we can findout the radius of all 11 particle.

for particle 1 : R1= 2m* v/q.B= 2R

similarly particle 2 :R2=R/2

particle 3 :R3= R

particle 4 :R4=3R

particle 5 :R5=4R

particle 6 : R6=(-2R)

particle 7 : R7=(-R/4)

particle 8: R8= (-R)

particle 9 : R9=(-3R)

particle 10 : R10=(-4R)

particle 11 : R11= infinity

Now the smallest semicircle size is R/4 and it is for a particle with negative charge. The smallest path in the figure is d. so it is for particle 7.

And we know negative particle will curve in one direction and postive particle will curve in other direction. so here since a negative paricle (7) follows path d , so negative particle goes in clockwise and positive particle goes in counter clock wise direction.

so, path of all particles are:

particle 1 : i

particle 2 : e

particle 3 : c

particle 4 : a

particle 5 : g

particle 6 : j

particle 7 : d

particle 8 : b

particle 9 : h

particle 10 : f

particle 11 : k

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