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Q10Q

Expert-verifiedFound in: Page 828

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**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.)**

Particles 1 to 11 corresponds to path i, e, c, a, g, j, d, b, h, f, k respectively.

Corresponding mass, velocity and charge of different particles are given in table.

**Using the relation ****28-16**** ****for radius find the radius of different particles and analyzing the given diagram find the corresponding paths of different particles.**

Formulae are as follow:

Where, *r* is radius, *B* is magnetic field, *v* is velocity, *m* is mass,* q* is charge on particle.

** **

$m={m}_{l}=8{N}_{1}=-q$

Using equation 28-16, find the radius of different paths.

For particle 1

m=2m,V=v,q=q

The path i shows the radius r=2. Hence particle 1 shows the path i

For particle 2,

The path e shows the radius r=0.5.

Hence, particle 2 shows the path e.

For particle 3,

The path c shows the radius r=1

Hence, particle 3 shows the path c.

For particle 4,,

m=3m,V=3v,q=3q

The path a shows the radius r=3

Hence, particle 4 shows the path a.

For particle 5

The path g shows the radius r=4

Hence, particle 5 shows the path g.

For particle 6,

The path j shows the radius r=-2

Hence, particle 6 shows the path j.

For particle 7,

The path d shows the radius r=0.25

Hence, particle 7 shows the path d

For particle 8

The path b shows the radius r=-1

Hence, particle 8 shows the path b

For particle 9,

The path h shows the radius r=-3

Hence, particle 9 shows the path h

For particle 10

$m={m}_{l}=8{N}_{1}=-q$$r=\frac{m\left(8v\right)}{-2qB}=-4\left(\frac{m}{qB}\right)$

The path shows the radius r=-4

Hence, particle 10 shows the path f

For particle 11

$m=3{m}_{|}={8}_{1}q=$0

$r=\frac{\left(3m\right)\left(3w\right)}{\left(0\right)B}=0$

The path shows the radius r=0

Hence, particle 11 shows the path k.

Hence, particles 1 to 11 corresponds to path i, e, c, a, g, j, d, b, h, f, k respectively.

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