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

We are given surface current density, K which is constant (K is negative) along the z-axis which is placed in x=a plane (the board which contains this density is neutral), in x=0 plane there's an infinite plane which is charged by a surface density [tex] \sigma[/tex] which is constant.

we have a particle with charge q and mass m which starts at rest at r=0.

Now,

1. given sigma find out what is the minimal K s.t the particles doesn't cross the boards.

2. given the K you found assume now K is twice the K in 1, and show that:

the minimal distance from the board with the current is

[tex]d_{min} = a- \frac{m\sigma}{\pi q (3\sigma^2 +\frac{4m\sigma}{\pi q a})}[/tex]

2. Relevant equations

There's a file with a picture of the system attached to this post here:

http://img2.tapuz.co.il/forums/1_143953502.pdf

It's question number 1, you shouldn't mind that the text is in hebrew, I translated what it asks in English.

3. The attempt at a solution

For 1 I thought of looking at the force euqation:

mv^2/a = qE+ qv x B where E is the electric field from the charged board and B is from the above board (situated at x=a), and then just need to find out when there's only one solution to this quadratic equation with regards to v, the veclotiy of the particle.

The problem arises when I need to prove (2).

Don't know how to do it.

Thanks.

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# Homework Help: Electromagnetism of particle problem

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