The Plasma Globe's Dancing Arc · AI Generator #GEN-4D75DF13

Physics · electromagnetism

Problem

In a plasma globe, high-frequency AC voltage creates dancing electric arcs between a central electrode and the glass sphere. Consider a simplified model where a sinusoidal voltage

V(t) = V_0 \sin(\omega t)

with amplitude

V_0 = 15.0\;\text{kV}

and frequency

f = 25.0\;\text{kHz}

is applied between two spherical electrodes separated by distance

d = 8.00\;\text{cm}

. The space between electrodes is filled with neon gas at low pressure. When the instantaneous electric field magnitude exceeds the breakdown field

E_b = 1.20 \times 10^5\;\text{V/m}

, a conducting plasma channel forms instantaneously, effectively short-circuiting the gap. The plasma channel persists until the current through it drops below the sustaining current

I_s = 2.50\;\text{mA}

, at which point it extinguishes and the gap becomes insulating again. The circuit can be modeled as the voltage source in series with a resistor

R = 100\;\text{k}\Omega

(representing the plasma channel resistance when conducting) and the electrode capacitance

C = 12.0\;\text{pF}

. (a) At what phase angle

\phi_1

(measured from

t = 0

) does breakdown first occur in each half-cycle? (b) At what phase angle

\phi_2

does the plasma extinguish in each half-cycle? (c) What is the average power dissipated in the plasma during one complete cycle?

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