Question

EM 3: Consider a solid insulating sphere with total charge Q and radius R. The volume charge density for the sphere is given by, $\rho(r) = \begin{cases} A \left(1 - \frac{r^2}{R^2} \right) & \text{for } r \le R \\ 0 & \text{for } r > R \end{cases}$ where A is a constant with the units of $\left[\frac{C}{m^3}\right]$. a) Determine the constant A in terms of total charge Q and radius R. b) Using Gauss's law, determine the electric field $\vec{E}(r)$ for all points in the regions $0 < r < R$ and $r > R$ c) Determine the electric potential $V(r)$ for all points in the regions $0 < r < R$ and $r > R$. d) Examine the continuity of the electric field and electric potential at the boundary of $r = R$. Are they continuous? Why or why not?

          EM 3: Consider a solid insulating sphere with total charge Q and radius R. The volume
charge density for the sphere is given by,
$\rho(r) = \begin{cases} A \left(1 - \frac{r^2}{R^2} \right) & \text{for } r \le R \\ 0 & \text{for } r > R \end{cases}$
where A is a constant with the units of $\left[\frac{C}{m^3}\right]$.
a) Determine the constant A in terms of total charge Q and radius R.
b) Using Gauss's law, determine the electric field $\vec{E}(r)$ for all points in the regions
$0 < r < R$ and $r > R$
c) Determine the electric potential $V(r)$ for all points in the regions $0 < r < R$ and
$r > R$.
d) Examine the continuity of the electric field and electric potential at the boundary
of $r = R$. Are they continuous? Why or why not?

EM 3: Consider a solid insulating sphere with total charge Q and radius R. The volume
charge density for the sphere is given by,
ρ(r) = A (1 - (r^2)/(R^2)) for r ≤ R
0 for r > R
where A is a constant with the units of [(C)/(m^3)].
a) Determine the constant A in terms of total charge Q and radius R.
b) Using Gauss's law, determine the electric field E⃗(r) for all points in the regions
0 < r < R and r > R
c) Determine the electric potential V(r) for all points in the regions 0 < r < R and
r > R.
d) Examine the continuity of the electric field and electric potential at the boundary
of r = R. Are they continuous? Why or why not?

Added by Thomas P.

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