Electricity and Magnetism · Problem 5.23

THE MAGNETIC FIELD — Edward Purcell & David Morin

Physics — E&M · two-views-of-an-oscilloscope

Problem

Two views of an oscilloscope ** In a high-voltage oscilloscope the source of electrons is a cathode at potential −125-125 kV with respect to the anode and the enclosed region beyond the anode aperture. Within this region there is a pair of parallel plates 5 cm long in the xx direction (the direction of the electron beam) and 8 mm apart in the yy direction. An electron leaves the cathode with negligible velocity, is accelerated toward the anode, and subsequently passes between the deflecting plates at a time when the potential of the lower plate is −120-120 V, that of the upper plate +120+120 V. Fill in the blanks. Use rounded-off constants: electron rest energy =5⋅105= 5 \cdot 10^5 eV, etc. When the electron arrives at the anode, its kinetic energy is \underline{\hspace{1cm}} eV, its total energy has increased by a factor of \underline{\hspace{1cm}}, and its velocity is \underline{\hspace{1cm}} cc. Its momentum is \underline{\hspace{1cm}} kg m/s in the xx direction. Beyond the anode the electron passes between parallel metal plates. The field between the plates is \underline{\hspace{1cm}} V/m; the force on the electron is \underline{\hspace{1cm}} newtons upward. The electron spends \underline{\hspace{1cm}} seconds between the plates and emerges, having acquired yy momentum of magnitude py=p_y = \underline{\hspace{1cm}} kg m/s. Its trajectory now slants upward at an angle θ=\theta = \underline{\hspace{1cm}} radians. A fast neutron that just happened to be moving along with the electron when it passed through the anode reported subsequent events as follows. ``We were sitting there when this capacitor came flying at us at \underline{\hspace{1cm}} m/s. It was \underline{\hspace{1cm}} m long, so it surrounded us for \underline{\hspace{1cm}} seconds. That didn't bother me, but the electric field of \underline{\hspace{1cm}} V/m accelerated the electron so that, after the capacitor left us, the electron was moving away from me at \underline{\hspace{1cm}} m/s, with a momentum of \underline{\hspace{1cm}} kg m/s.''

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