The equation you provided is missing some closing brackets and exponents. Here is the corrected equation:
![\displaystyle \text{Electric field inside a plasma: } \vec{E}(\vec{r}) = -(q)/(4\pi\varepsilon_(0)\kappa) \left[\frac{e^{-(r)/(\lambda_(D))}}{r^(2)}+\frac{e^{-(r)/(\lambda_(D))}}{\lambda_(D) r}\right] \hat{r} = kq\left[\frac{e^{-(r)/(\lambda_(D))}}{r^(2)}+\frac{e^{-(r)/(\lambda_(D))}}{\lambda_(D) r}\right] \hat{r}](https://img.qammunity.org/2024/formulas/physics/high-school/s6tsdct2f2vxuzdyyg03raywz2qq3mz1cm.png)
Please note that the equation assumes the presence of charged particles inside a plasma and describes the electric field at a specific position
. The terms
,
,
,
, and
represent the charge of the particle, vacuum permittivity, dielectric constant, Debye length, and Coulomb's constant, respectively.

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