In an infinitely large uniform medium with a permittivity of ε, there is a spherical cavity with a radius of $R$, and an externally applied uniform electric field $E_0$. Determine the electric field intensity inside and outside the cavity is _____.

Options:
A. The electric field intensity inside the cavity is
$$E_{\mathrm{i}}=\frac{5\varepsilon}{\varepsilon+3\varepsilon_{0}}E_{0}\:,\quad r<\stackrel{\cdot}{R}\quad,$$
The electric field intensity outside the cavity is
$$\begin{aligned}&E=E_{0}+\frac{\varepsilon-\varepsilon_{0}}{5\varepsilon+\varepsilon_{0}}\frac{R^{2}}{r^{2}}E_{0}\biggl[E_{0}-\frac{(E_{0}\cdot r)r}{r^{2}}\biggr],\quad r>R&\end{aligned}$$
B. The electric field intensity inside the cavity is
$$E_{\mathrm{i}}=\frac{\varepsilon}{3\varepsilon_{0}}E_{0}\:,\quad r<\stackrel{\cdot}{R}\quad,$$
The electric field intensity outside the cavity is
$$\begin{aligned}&E=E_{0}+\frac{\varepsilon_{0}-\varepsilon}{2\varepsilon+3\varepsilon_{0}}\frac{R^{5}}{r^{5}}E_{0}\biggl[E_{0}-\frac{4(E_{0}\cdot r)r}{r^{3}}\biggr],\quad r>R&\end{aligned}$$
C. The electric field intensity inside the cavity is
$$E_{\mathrm{i}}=\frac{3\varepsilon_{0}}{\varepsilon+\varepsilon_{0}}E_{0}\:,\quad r<\stackrel{\cdot}{R}\quad,$$
The electric field intensity outside the cavity is
$$\begin{aligned}&E=E_{0}+\frac{\varepsilon_{0}-\varepsilon}{2\varepsilon+2\varepsilon_{0}}\frac{R^{3}}{r^{3}}E_{0}\biggl[E_{0}-\frac{4(E_{0}\cdot r)r}{r^{2}}\biggr],\quad r>R&\end{aligned}$$
D. The electric field intensity inside the cavity is
$$E_{\mathrm{i}}=\frac{\varepsilon_{0}}{2\varepsilon}E_{0}\:,\quad r<\stackrel{\cdot}{R}\quad,$$
The electric field intensity outside the cavity is
$$\begin{aligned}&E=E_{0}+\frac{\varepsilon-\varepsilon_{0}}{4\varepsilon+\varepsilon_{0}}\frac{R^{3}}{r^{3}}E_{0}\biggl[E_{0}-\frac{3(E_{0}\cdot r)r}{r^{2}}\biggr],\quad r>R&\end{aligned}$$
E. The electric field intensity inside the cavity is
$$E_{\mathrm{i}}=\frac{3\varepsilon}{2\varepsilon+\varepsilon_{0}}E_{0}\:,\quad r<\stackrel{\cdot}{R}\quad,$$
The electric field intensity outside the cavity is
$$\begin{aligned}&E=E_{0}+\frac{\varepsilon-\varepsilon_{0}}{2\varepsilon+\varepsilon_{0}}\frac{R^{3}}{r^{3}}E_{0}\biggl[E_{0}-\frac{3(E_{0}\cdot r)r}{r^{2}}\biggr],\quad r>R&\end{aligned}$$
F. The electric field intensity inside the cavity is
$$E_{\mathrm{i}}=\frac{4\varepsilon}{\varepsilon+2\varepsilon_{0}}E_{0}\:,\quad r<\stackrel{\cdot}{R}\quad,$$
The electric field intensity outside the cavity is
$$\begin{aligned}&E=E_{0}+\frac{\varepsilon-\varepsilon_{0}}{3\varepsilon+2\varepsilon_{0}}\frac{R^{4}}{r^{4}}E_{0}\biggl[E_{0}-\frac{(E_{0}\cdot r)r}{r^{2}}\biggr],\quad r>R&\end{aligned}$$
G. The electric field intensity inside the cavity is
$$E_{\mathrm{i}}=\frac{\varepsilon+\varepsilon_{0}}{3\varepsilon}E_{0}\:,\quad r<\stackrel{\cdot}{R}\quad,$$
The electric field intensity outside the cavity is
$$\begin{aligned}&E=E_{0}+\frac{\varepsilon_{0}-\varepsilon}{4\varepsilon+2\varepsilon_{0}}\frac{R^{4}}{r^{4}}E_{0}\biggl[E_{0}-\frac{2(E_{0}\cdot r)r}{r^{2}}\biggr],\quad r>R&\end{aligned}$$
H. The electric field intensity inside the cavity is
$$E_{\mathrm{i}}=\frac{\varepsilon_{0}}{5\varepsilon+2\varepsilon_{0}}E_{0}\:,\quad r<\stackrel{\cdot}{R}\quad,$$
The electric field intensity outside the cavity is
$$\begin{aligned}&E=E_{0}+\frac{\varepsilon-\varepsilon_{0}}{5\varepsilon_{0}+\varepsilon}\frac{R^{3}}{r^{3}}E_{0}\biggl[E_{0}-\frac{3(E_{0}\cdot r)r}{r^{4}}\biggr],\quad r>R&\end{aligned}$$
I. The electric field intensity inside the cavity is
$$E_{\mathrm{i}}=\frac{2\varepsilon_{0}}{\varepsilon+\varepsilon_{0}}E_{0}\:,\quad r<\stackrel{\cdot}{R}\quad,$$
The electric field intensity outside the cavity is
$$\begin{aligned}&E=E_{0}+\frac{\varepsilon_{0}-\varepsilon}{3\varepsilon+\varepsilon_{0}}\frac{R^{2}}{r^{2}}E_{0}\biggl[E_{0}-\frac{2(E_{0}\cdot r)r}{r^{3}}\biggr],\quad r>R&\end{aligned}$$
J. The electric field intensity inside the cavity is
$$E_{\mathrm{i}}=\frac{2\varepsilon}{4\varepsilon+3\varepsilon_{0}}E_{0}\:,\quad r<\stackrel{\cdot}{R}\quad,$$
The electric field intensity outside the cavity is
$$\begin{aligned}&E=E_{0}+\frac{\varepsilon_{0}-\varepsilon}{3\varepsilon+\varepsilon_{0}}\frac{R^{6}}{r^{6}}E_{0}\biggl[E_{0}-\frac{5(E_{0}\cdot r)r}{r^{3}}\biggr],\quad r>R&\end{aligned}$$
Answer: E