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A beam of protons with various speeds is directed in the positive x direction. The beam enters a region with a uniform magnetic field of magnitude 0.46 T pointing in the negative z direction, as indicated in Figure. It is desired to use a uniform electric field (in addition to the magnetic field) to select from this beam only those protons with a speed of 1.40 x 10⁵ m/s; that is, only these protons should be undeflected by the two fields.

458_A beam of protons with various speeds.gif

(a) Determine the electric field that yields the desired result.

(b) Suppose the electric field is to be produced by a parallel-plate capacitor with a plate separation of 2.5 cm. What potential difference is required between the plates?

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