13.3 Solutions
601
13.7 q E = q v B
∴
B =
E
v
=
1500
3000
= 0.5 T
13.8 (a) v =
rqB
m
=
1.9 × 1.6 × 10 −19 × 3 × 10 −5
9.1 × 10 −31
= 10 7 m/s
(b) t =
2πr
v
=
2π × 1.9
10 7
= 1.19 × 10 −6 s = 1.19 μs
13.9 B =
2π m f
q
=
2π × 2.0141 × 1.66 × 10 −27 × 5 × 10 6
1.6 × 10 −19
= 0.656 Wb/m
2
K =
1
2
q 2 r 2 B 2
m
=
1
2
×
(1.6 × 10 −19 ) 2 (0.762) 2 (0.325) 2
2.0141 × 1.66 × 10 −27
= 4.696 × 10
−13 J
= 2.9 MeV
13.10 For deuterons
B =
2π f m
q
=
2π × 11.5 × 10 6 × 2.014 × 1.66 × 10 −27
1.6 × 10 −19
= 1.509 Wb/m
2
For protons
f =
q B
2π m
=
1.6 × 10 −19 × 1.509
2π × 1.66 × 10 −27 = 2.316 × 10
7 c/s = 23.16 Mc/s
13.11 (a) f =
Bq
2π m
=
1.5 × 1.6 × 10 −19
2π × 3.32 × 10 −27 = 11.5 × 10 6 c/s = 11.5 Mc/s
(b) K =
1
2
q 2 r 2 B 2
m
=
1
2
(1.6 × 10 −19 × 0.5 × 1.5) 2
3.32 × 10 −27
= 21.69 × 10 −13 J =
13.56 MeV
13.12 i =
q
t
=
1.6 × 10 −19
1.5 × 10 −16 = 1.06 × 10 −3 A
13.13 (i) Magnetic force, F M = qVB
Electric force, F E = q E
For no deflection, F M = F E
∴
qvB = q E
∴
v =
E
B
=
80 × 10 3
0.4
= 2 × 10
5 m/s
(ii) mv 2
r
= q v B
∴
q
m
=
v
Br
=
E
B 2 r
=
80 × 10 3
(0.4) 2 (1.14 × 10 −2 )
= 4.38 × 10
7 C/kg