As soon as possible, Handwrite, more details please **Spherical Charge System with Zero External Field:**What spherical charge distribution creates the field given at right, where \( r \) is defined as in spherical coordinates? Note the discontinuity in the field: what does this require at the surface?\[\vec{E}(r) = \begin{cases} \frac{\rho_0}{3 \varepsilon_0} \hat{r} & r \le a \\0 & r > a\end{cases}\]In this scenario, we are examining a spherical charge system with no external field. The electric field \(\vec{E}(r)\) is different inside and outside the sphere:- **For \( r \le a \):** The electric field vector \(\vec{E}(r)\) is given by \(\frac{\rho_0}{3 \varepsilon_0} \hat{r}\). Here, \(\rho_0\) is the charge density, \(\varepsilon_0\) is the permittivity of free space, and \(\hat{r}\) is the radial unit vector in spherical coordinates. This expression indicates a uniform electric field inside a sphere of radius \( a \).- **For \( r > a \):** The electric field is zero, implying that the influence of the charge distribution does not extend beyond the surface of the sphere.This system presents a discontinuity at the surface \( r = a \), which must be addressed to ensure physical consistency, possibly through boundary conditions or surface charge considerations.

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hand write, more details, Step by step solutions Spherical Charge System with Zero External Field: What spherical charge distribution creates the field given at right, where r is defined as in spherical coordinates? Note the discontinuity in the field: what does this require at the surface? E(T) = Porsa 380 0 r>a

hand write, more details, Step by step solutions Spherical Charge System with Zero External Field: What spherical charge distribution creates the field given at right, where r is defined as in spherical coordinates? Note the discontinuity in the field: what does this require at the surface? E(T) = Porsa 380 0 r>a