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Homework Statement
A beam of electrons is fired into a rectangular region of space that contains a uniform magnetic field in the z direction. The electrons are moving in the +x direction, as shown. The speed of the electrons in the beam is 6.00 × 106 m/s. The mass of an electron is me = 9.11 × 10−31 kg. The magnitude of the magnetic field in the rectangular region of space is 1.50 × 10−2 T. The rectangular region has a width d.
What is the maximum value of d for which the electron beam will make it through to the other side of this rectangular region, and continue on to the right of the region?
Homework Equations
⃗v=E⃗/B⃗1
(Equations provided)
F⃗m = q⃗vB⃗  sin(θ)
F⃗m = ILB⃗  sin θ r = m  ⃗v 
qB⃗  r = m  ⃗v ⊥  qB⃗ 
F⃗E=F⃗B −→ qE⃗=q⃗vB⃗1 −→ ⃗v=E⃗/B⃗1  m⃗  = N I A
τ = NIAB⃗sinθ = m⃗ B⃗sinθ
 B⃗  = μ 0 I 2πr
 B⃗  = μ 0 N I 2r
 B⃗  = μ 0 N I L
Φv =⃗vAcos(θ)
ΦB =B⃗Acos(θ)
E = N∆Φ ∆t
I = V/R
I = E/R (linear DC generator)
E = BvL (linear DC generator)
I = E/R = BvL/R (linear DC generator)
Fm = ILB = (B2vL2)/R (linear DC generator)
Pmechanical = Fappl v Pelectrical = IV = IE
ΦB = BA cos(ωt) (rotary AC generator)
E = (NBAω)sin(ωt) (rotary AC generator)
￼￼￼￼￼￼I = E/R = (NBAω/R) sin(ωt) 1Tesla(1T)=1 N
μ0 =4π×10−7 Tm A
The Attempt at a Solution
E=6.00 x 10^6m/s x 1.50 x 10^2 T
90000 T x m/s
Ok the problem I am having is relating distance to any equation I have. In previous problems I have worked, none of them had distance as part of the problem. If someone could just give me a hint or something about how to relate distance to the problem, that would be much appreciated.
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