9.3 Solutions
523
Fig. 9.10
9.72 t =
2u sin α
α
=
2u sin α
Ee
.m
Where the acceleration α = Ee/m
t =
2 × 8 × 10
5 sin 30
◦
× 9.1 × 10
−31
50 × 1.6 × 10 −19
= 91 × 10
−9 s = 91 ns
9.73 The component of the velocity, ⊥ to the field is v sin θ . Equating the centripetal force to the magnetic force
mv
2
⊥ = qv ⊥ B R
R = mv ⊥ /qB = v sin θ/(q/m)B
=
3 × 10
5 sin 30
0
10 8 × 0.3
= 0.5 × 10
−2 m
= 0.5 cm
9.74 p = 0.3BR = (0.3)(10
−4 )(6.4 × 10
6 ) = 192 GeV/c
T ≈ 192 GeV
9.75 Cosmic ray flux = 1 cm
−2 s
−1
= 10
4 m
−2 s
−1
Earth’s surface area, A = 4 π R
2
= 4π(64 × 10
5 )
2
= 5.144 × 10
14 m
2
Cosmic rays incident on earth’s surface
= 5.144 × 10
14
× 10
4
= 5.144 × 10
18 m
−2 s
−1
Cosmic rays energy delivered to earth
= 5.144 × 10
18
× 3 GeV s
−1
= 1.5432 × 10
19 GeV s
−1
= 1.5432 × 10
19
× 1.6 × 10
−10 J s
−1
= 2.47 × 10
9 W
= 2.47 GW.