Physics · Electricity and magnetism · Grade 8

Electric current in vacuum and gases

How does a neon sign light up, and how is the beam drawn in an old television tube?

The situation

In the evening, advertising signs glow red-orange along the city streets: current is passing through rarefied neon gas in a glass tube. In old televisions an “electron gun” behind the picture tube fired a beam of electrons at the screen and drew the picture point by point. A welder strikes a dazzling arc between an electrode and the metal. Normally neither a vacuum nor a gas conducts current — so where do the charge carriers come from in these cases, and what does the current depend on?

Topic

Electric current in vacuum and gases. Neon sign, an old television tube and a welding arc

Key ideas

Thermionic emission
Cathode-ray tube
Gas discharge

Formulas

j_{s} = A T^{2} e^{- W / (k T)}

Richardson–Dushman formula: saturation current density; $W$ is the work function.

I = K U^{3 / 2}

Boguslavsky–Langmuir “3/2 law”: diode current limited by space charge.

I_{a} = K {(U_{g} + \frac{U_{a}}{μ})}^{3 / 2}, μ = S R_{i}

Triode: the grid voltage acts $μ$ times more strongly than the anode voltage; $S$ is the slope of the characteristic and $R_{i}$ is the internal resistance.

y = \frac{l L}{2 d} \cdot \frac{U_{y}}{U_{a}}, \frac{e}{m} = \frac{U_{y}^{2}}{2 U_{a} d^{2} B^{2}}

Deflection of an electron beam and Thomson's method (at $e E = e v B$ the beam is not deflected).

U_{br} = \frac{B p d}{\ln (A p d) - \ln \ln (1 + 1 / γ)}

Paschen's law: the breakdown voltage of a gas depends only on the product of pressure and distance.

Theory

Current in a vacuum: electron emission

There are no free charges in a vacuum — they have to be “pulled out” of an electrode. To leave a metal, an electron must do the work function $W$ (a few eV). Electrons “evaporate” from a heated cathode — this is thermionic emission; the saturation current depends exponentially on temperature according to the Richardson–Dushman formula. Other kinds of emission: photoemission under the action of light (the photoelectric effect), secondary emission from impact, and, in a very strong field ( $\sim 10^{9}$ V/m, a pointed cathode), electrons tunnel through the barrier — field emission (electron microscopes, the Fowler–Nordheim current). The difference between the work functions of two metals gives a contact potential difference $(W_{1} - W_{2}) / e$ when they touch; thermoelectric effects (Seebeck, Peltier, Thomson) are based on this — see other experiments for details.

Vacuum diode: the 3/2 law and saturation

The electrons emitted around the cathode form a cloud of space charge and repel the ones that follow. At small $U_{a}$ the current is limited by the cloud: $I = K U^{3 / 2}$ (Boguslavsky–Langmuir). As $U_{a}$ grows, the cloud is drawn away and finally all the electrons emitted by the cathode reach the anode — the saturation current $I_{s}$ ; it depends only on the temperature and material of the cathode. At reverse voltage the electrons are repelled: the diode passes current in one direction only — a rectifier. A semiconductor diode works in the same way, but needs no heating, opens at ≈ 0.6 V and is much more compact. Determining the work function: record $I_{s}$ at different $T$ and plot $\ln (I_{s} / T^{2})$ against $1 / T$ — the gradient is $- W / k$ .

The triode — the first amplifier

If a sparse wire grid is placed close to the cathode, a small voltage on it controls the space-charge barrier: a change of 1 V in $U_{g}$ changes the anode current as much as a change of $μ$ V in $U_{a}$ . Parameters: slope $S = Δ I_{a} / Δ U_{g}$ , internal resistance $R_{i} = Δ U_{a} / Δ I_{a}$ , amplification factor $μ = S R_{i}$ . If a load $R_{a}$ is put into the anode circuit, a small signal on the grid is amplified $K = μ R_{a} / (R_{a} + R_{i})$ times — see it in “Amplifier” mode. Triodes were the basis of radio, television and the first computers. Model: the grid current at a positive grid voltage is not taken into account.

The cathode-ray tube and the oscilloscope

An electron gun (cathode, modulator, accelerating anodes) forms a thin beam: $v = \sqrt{2 e U_{a} / m}$ . Between the deflecting plates the beam bends along a parabola, and on the screen $y = l L U_{y} / (2 d U_{a})$ . If a sawtooth (sweep) voltage is applied to the X plates, the spot moves evenly across the screen and traces the shape of the Y signal against time — this is the oscilloscope. If sinusoidal signals are applied to both pairs of plates, Lissajous figures appear: their shape depends on the ratio of the frequencies and the phase difference. In a television picture tube the beam is deflected by magnetic coils. Electron beams are used in electron microscopes, X-ray tubes, and for welding and melting in a vacuum. Model: non-relativistic, small deflection angles.

Specific charge of the electron e/m

Thomson's method: a magnetic field $B$ perpendicular to the electric field is applied in the region of the Y plates. When $e E = e v B$ the beam is not deflected, so $v = E / B = U_{y} / (d B)$ . From $v^{2} = 2 e U_{a} / m$ , $e / m = U_{y}^{2} / (2 U_{a} d^{2} B^{2}) \approx 1.76 \cdot 10^{11}$ C/kg. The magnetron method: if a magnetic field is applied along the axis of the diode, the electrons travel along curved paths; at $B > B_{c r} = \sqrt{8 m U / e} / r_{a}$ they turn back before reaching the anode and the current drops sharply: $e / m = 8 U / (B_{c r}^{2} r_{a}^{2})$ . In “Diode” mode, increase $B$ and find the value at which the current falls by half.

Current in gases: ionisation, types of discharge, plasma

Gas molecules are neutral, but ionisers (flame, ultraviolet, X-rays, radioactive radiation) split them into ions and electrons; when ions and electrons meet they combine again — recombination. While the ioniser is working a weak current flows, and it stops when the ioniser is switched off — a non-self-sustaining discharge (as the voltage rises the current saturates). If the voltage is raised further, electrons gain enough energy over their mean free path to ionise a molecule — an electron avalanche begins, the ions knock new electrons out of the cathode, and the discharge becomes self-sustaining (Paschen's law). A glow discharge gives light in a rarefied gas (neon — red-orange, argon — violet, mercury vapour — bluish); an arc has a large current and a low voltage (tens of volts) — welding and arc furnaces; a spark is a short-lived channel at high pressure (lightning is a gigantic spark); a corona forms in a strong field around a thin wire or a point (losses on power lines, electrostatic precipitators). An ionised, overall neutral gas is plasma: the positive column of a discharge, the lightning channel, the Sun. Model: the I–V characteristic is schematic, $γ$ = 0.02, and the onset of corona follows Peek's formula.

Did you know?

In 1883 Thomas Edison observed current passing through a vacuum near a glowing filament in his experiments with an incandescent lamp — this phenomenon is also called the “Edison effect”.
In 1897 Joseph John Thomson measured the deflection of cathode rays in electric and magnetic fields, established that they are a stream of charged particles and determined their ratio e/m — this is how the electron was discovered.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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Capacitor and capacitance — Grade 8
Circuits and Kirchhoff's rules — Grade 8
Electric current in metals — Grade 8
Electrolysis, Faraday's laws — Grade 8
Magnetic field — Grade 8
Electromagnet and relay — Grade 8
Shake torch — Grade 10
Self-induction — Grade 10
Magnetic properties of matter — Grade 10