- #1
touqra
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A plasma is described by the dielectric function
[tex] \epsilon (\omega) = \epsilon_0 (1-\frac{\omega_p^2}{\omega^2}) [/tex]
where [tex] \omega_p [/tex] is a constant. Any attempt to establish a voltage
[tex] V(t) = V cos \omega t [/tex] across the plasma generates a region of vacuum called the "sheath" on either side of the plasma volume.
Derive expressions for the uniform electric field [tex] E_p (t) = E_p cos \omega t [/tex] in the plasma and for [tex] E_s (t) = E_s cos \omega t [/tex] in the sheath. Assume that there is no free charge anywhere. Assume that [tex] \omega_p [/tex] is small enough that an electrostatic approximation is always valid.
I don't really understand. Isn't the electric field is stated in the question already ?
[tex] \epsilon (\omega) = \epsilon_0 (1-\frac{\omega_p^2}{\omega^2}) [/tex]
where [tex] \omega_p [/tex] is a constant. Any attempt to establish a voltage
[tex] V(t) = V cos \omega t [/tex] across the plasma generates a region of vacuum called the "sheath" on either side of the plasma volume.
Derive expressions for the uniform electric field [tex] E_p (t) = E_p cos \omega t [/tex] in the plasma and for [tex] E_s (t) = E_s cos \omega t [/tex] in the sheath. Assume that there is no free charge anywhere. Assume that [tex] \omega_p [/tex] is small enough that an electrostatic approximation is always valid.
I don't really understand. Isn't the electric field is stated in the question already ?
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