A proton, that is accelerated from rest through a potential of 19.0 kV enters th

Question

A proton, that is accelerated from rest through a potential of 19.0kV enters the velocity filter, consisting of a parallel-plate capacitor and a magnetic field, shown below.

The E-field between the parallel capacitor plates is 5.5x105N/C. What B-field is required so that the protons are not deflected? (Ignore relativistic effects for high velocities.)

A proton, that is accelerated from rest through a potential of 19.0kV enters the velocity filter, consisting of a parallel-plate capacitor and a magnetic field, shown below. The E-field between the parallel capacitor plates is 5.5x10^5 N/C. What B-field is required so that the protons are not deflected? (Ignore relativistic effects for high velocities.)

Explanation / Answer

From the conservation of energy, we can find the velocity of the proton,

                qV = 0.5mv2

(1.6 X 10-19)(19000) = (0.5)(1.67 X 10-27)(v2)

                               v = 1.92 X 106 m/s

Then, for the case, proton not to be deflected, the Electric and Magnetic fields are balanced by the equation

      v = E/B

(1.92X 106) = (5.5 X 105)/B

                 B = 0.286 T

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