(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

|⃗v|=|E⃗|/|B⃗1|

(Equations provided)

|F⃗m| = |q||⃗v||B⃗ || sin(θ)|

|F⃗m| = IL|B⃗ || sin θ| r = m | ⃗v |

|q||B⃗ | r = m | ⃗v ⊥ | |q||B⃗ |

|F⃗E|=|F⃗B| −→ q|E⃗|=q|⃗v||B⃗1| −→ |⃗v|=|E⃗|/|B⃗1| | m⃗ | = N I A

τ = NIA|B⃗||sinθ| = |m⃗ ||B⃗||sinθ|

| B⃗ | = μ 0 I 2πr

| B⃗ | = μ 0 N I 2r

| B⃗ | = μ 0 N I L

Φv =|⃗v|Acos(θ)

ΦB =|B⃗|Acos(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

3. 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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# Homework Help: Max distance of rectangle that electron beam can pass through

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