602
13 Electromagnetism I
13.14 (a) F = qE + qv × B
(b) In the electric field energy acquired, K = qV
∴
p =
√
2m K =
2mqV.
(1)
In the magnetic field
p = qBr
(2)
Combining (1) and (2)
r =
2mV
q B 2
13.15 Let the isotopes 235 U and 238 U be called 1 and 2, respectively. In the magnetic field the momenta are given by
p 1 = qBr 1 , p 2 = qBr 2
p 2 − p 1 = qB (r 2 − r 1 ) = 1.6 × 10
−19
× 0.2 × 2 × 10
−3
(13.26)
= 6.4 × 10
−21 kg m/s.
(1)
In the electric field
qV =
p 2
1
2m 1
=
p 2
2
2m 2
(2)
∴ p 2 = p 1
m 2
m 1
= p 1
3.95 × 10 −25
3.90 × 10 −25 = 1.00639 p 1 .
(3)
Combining (1) and (3)
p 1 = 1.00159 × 10
−19 kg m/s.
(4)
Substituting (4) into (2)
V =
(10 −19 ) 2
2 × 1.6 × 10 −19 × 3.90 × 10 −25 = 8 × 10
4 V
13.16 (a) F = q v × B
If B is perpendicular to v, then the particle would move in a circle.
Centripetal force = magnetic force
mv 2
r
= qv B → r =
mv
q B
13 Electromagnetism I
13.14 (a) F = qE + qv × B
(b) In the electric field energy acquired, K = qV
∴
p =
√
2m K =
2mqV.
(1)
In the magnetic field
p = qBr
(2)
Combining (1) and (2)
r =
2mV
q B 2
13.15 Let the isotopes 235 U and 238 U be called 1 and 2, respectively. In the magnetic field the momenta are given by
p 1 = qBr 1 , p 2 = qBr 2
p 2 − p 1 = qB (r 2 − r 1 ) = 1.6 × 10
−19
× 0.2 × 2 × 10
−3
(13.26)
= 6.4 × 10
−21 kg m/s.
(1)
In the electric field
qV =
p 2
1
2m 1
=
p 2
2
2m 2
(2)
∴ p 2 = p 1
m 2
m 1
= p 1
3.95 × 10 −25
3.90 × 10 −25 = 1.00639 p 1 .
(3)
Combining (1) and (3)
p 1 = 1.00159 × 10
−19 kg m/s.
(4)
Substituting (4) into (2)
V =
(10 −19 ) 2
2 × 1.6 × 10 −19 × 3.90 × 10 −25 = 8 × 10
4 V
13.16 (a) F = q v × B
If B is perpendicular to v, then the particle would move in a circle.
Centripetal force = magnetic force
mv 2
r
= qv B → r =
mv
q B