Question

Whats wrong with the equation?

charged particles inside plasma
\[ \text { - } \vec{E}(\vec{r})=\frac{q}{4 \pi \varepsilon_{0} \kappa}\left[\frac{e^{-\frac{r}{\lambda_{D}}}}{r^{2}}+\frac{e^{-\frac{r}{\lambda_{D}}}}{\lambda_{D} r}\right] \hat{r}=k q\left[\frac{e^{-

Answer 1

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}`

Please note that the equation assumes the presence of charged particles inside a plasma and describes the electric field at a specific position
`\displaystyle\sf \vec{r}`. The terms
`\displaystyle\sf q`,
`\displaystyle\sf \varepsilon_(0)`,
`\displaystyle\sf \kappa`,
`\displaystyle\sf \lambda_(D)`, and
`\displaystyle\sf k` represent the charge of the particle, vacuum permittivity, dielectric constant, Debye length, and Coulomb's constant, respectively.

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