1. Electrons can be “boiled off” of a wire by heating the wire to sufficiently h

Question

1. Electrons can be “boiled off” of a wire by heating the wire to sufficiently high temperature (typically well over 1000? C). Typically the electrons leave the wire with a fairly low speed which can be approximated as zero. In many devices where this is done the hot wire is also maintained at some voltage which causes the electrons to accelerate away from the wire.
Suppose electrons are boiled off of a wire that is held at an unknown voltage. The electrons accelerate away and eventually hit a metal plate which is grounded. By convention we define the grounded plate as having V = 0.

(a) Is the voltage at the hot wire positive or negative? Explain.

(b) There are various ways that we could measure the speed of the electrons as they impact the grounded plate. Suppose we determine that the electrons have a speed of 2.96 × 107 m/s just before hitting the plate. What is the voltage at the hot wire?

Explanation / Answer

(a) the hot wire is negative, that is why the negatively-charged electrons accelerate away from it towards ground

(b) electrons traveling at that speed have a kinetic energy of ½mv2 =

(0.5)(9.11 * 10-31 kg)(2.96 * 107 m/s)2 = 3.99 * 10-16 J

But that many joules is equal to energy of 2491 eV (1 eV = 1.602 * 10-19 J) so the electron must have experienced a potential of 2491 volts. Or include the negative sign, -2491 volts.

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