Question

The voltage between the anode and the cathode of a vacuum-tube diode is U, and the anode current is I.

Determine the mean pressure pn., of electrons on the anode surface of area S.

Answer 1

Since the anode current is I, the number of charge carriers (electrons) n arriving at the anode per unit time can be found from the formula

where e is the charge of a carrier. The momentum Δp transferred by the charge carriers to the anode per unit time is

Δp = nmv,

where m is the mass of a carrier, and v. is its velocity. This momentum is equal to the mean force exerted on the anode by the charge carriers precipitating on it. Since mv²/2 = | e | U, where U is the potential difference between the cathode and the anode, the mean pressure pm exerted by electrons on the anode can be determined from the formula