Charged particles are accelerated through a potential difference (V_{0}) before falling onto a lens consisting of an

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Charged particles are accelerated through a potential difference \(V_{0}\) before falling onto a lens consisting of an aperture of height \(y_{0}\) and thickness \(w\), as shown in the figure.

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There is a uniform electric field \(\mathbf{E}_{1}\) and \(\mathbf{E}_{2}\) on the left and right of the aperture respectively, as depicted. The figure also shows the trajectory of a charged particle of charge \(q\) emerging a distance \(x_{1}\) from the aperture on the left and focusing a distance \(x_{2}\) on the right. Assume \(V_{0} \gg E_{1} x_{1}\) and \(E_{2} x_{2}\), and \(x_{1}\) and \(x_{2} \gg y_{0}\).

(a) Using \(abla \cdot \mathbf{E}=0\), show that inside the aperture, we have

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Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

Authors: T. M. Helliwell, V. V. Sahakian

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