Fall 2006 4 Em

There is one conducting sheet in the plane z = 0 and another in the plane z = L. The lower sheed (i.e. z = 0) carries charge per unit area $\sigma$ and the upper one carries $-\sigma ,$ where $\sigma > 0$. Also, the lower sheet carries current per unit length $\hat{y} K$ and the upper one carries $-\hat{y} K$. The sheets extend to $\pm \infty$ in x and y.

(a) Determine the scalar potential and the vector potential in the region between the two sheets.

(b) Suppose that the particle is ejected from the lower sheet with velocity $\vec{v}=\hat{z}v_0$. What is the minimum value of $v_0$ such that the electron will reach the upper sheet? Hint: One way to solve this problem is to start with the Lagrangian.

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