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## Homework Statement

A slab beam of electrons of thickness

**a**, width

**w >> a**, charge density

(-ρ

_{b}), (Take ρ

_{b}to be positive.) and velocity

**v**

_{b}

**e**

_{z}passes through a channel of

neutralizing ions with charge density f*ρ

_{b}where f is some number between zero and one

(all parameters given above apply in the "lab" frame).

- Calculate the electric and magnetic fields produced by this combination of charges and currents in the region y << w / 2 .
- Find f such that there is no net force on any electron in the beam.

## Homework Equations

F[/B] = q(

**E**+

**v**

**x B**)

## The Attempt at a Solution

I have an idea as how to begin. But I am not very sure about it.

At any instant of time the new current flowing is given by (ρ

_{b}- f *ρ

_{b})*w*a*v

_{b}. If this is the current, then the magnetic field is given by Biot Savarts law (μ

_{o}/4π)*I/2R ? I just don't get this .

Can anybody guide me on how to start ?