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A beam of protons with various speeds is directed in the positive x direction. T

ID: 1693636 • Letter: A

Question

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 0.56 T pointing in the negative z direction, as indicated in the 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 1.37 x 10^5 m/s; that is, only these protons should be undeflected by the two fields. (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?
kV (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?
kV (c) Which plate in the figure should be positively charged?

CORRECT ANSWER: TOP PLATE
Explain. (c) Which plate in the figure should be positively charged?

CORRECT ANSWER: TOP PLATE
Explain.

Explanation / Answer

Given that magnetic field B = -(0.56 T)k speed of the proton is                     v = (1.37 x 10^5 m/s)i --------------------------------------------------------------------------- a) The electric field is             E = vXB                 = [ (1.37 x 10^5 m/s)i] x [ -(0.56 T)k]                 = (0.7672x 10^5) j N/C b) The potential difference between the plates is          V = Ed             = (0.7672x 10^5 N/C)(0.025 m )             = 1918 V c)  top plate
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