ˆB F qv B q v v B qv B qv n = × = + × = × = mv mv qB v F qv B r r m r

r
r
r r
r r
r r
FB = qv × B = q ( vP + v⊥ ) × B = qv⊥ × B = qv⊥B nˆ
B
vP
v
θ
FB = qvsenθ B
v⊥
mv⊥2
FB =
r
B
FB
r
Por otro lado
∴ qBr =
mv⊥2
→ qv⊥ B =
r
→
qB v⊥
=
m
r
qBr = mvsenθ
K = ∆U
2U
senθ
m
o sea,
→
1 2
2U
mv = U → v =
2
m
2mU senθ
r=
qB
Como v⊥ =
2π r
T
→ T=
2π r
m
= 2π ⋅
v⊥
qB
Además, en el tiempo T la partícula “avanza” p con rapidez vP = v cosθ o sea,
p = v cos θ ⋅ T =
2U
2π m
2π
cos θ ⋅
= 2mU cos θ ⋅
m
qB
qB
Numéricamente
2π ⋅ 9,11 ⋅10−31
−6
T=
=
8.9
×
10
[ s]
−19
−6
1.6 ⋅ 10 ⋅ 400 ⋅10
p = 2 ⋅ 9.11⋅ 10−31 ⋅ 20 ⋅1.6 ⋅10−19 cos85
= 6.6 ⋅ 10−3 [ m ]
2π
=
− 19
−6
1.6 ⋅10 ⋅ 400 ⋅10
2 ⋅ 9.11 ⋅10−31 ⋅ 20 ⋅1.6 ⋅10−19 sen85
−2
r=
=
3.8
⋅
10
[ m]
−19
−6
1.6 ⋅ 10 ⋅ 400 ⋅10