Fields from symmetry in code

You will write three functions for the fields that Gauss's law gives. Use $\varepsilon_0 = 8.85 \times 10^{-12}\ \text{C}^2/(\text{N m}^2)$.

The idea. A long wire with a charge $\lambda$ on each metre has $E = \lambda/(2\pi\varepsilon_0 r)$. A large sheet with a charge $\sigma$ on each square metre has $E = \sigma/(2\varepsilon_0)$. A solid insulating ball of radius $R$ with a total charge $Q$ has $E = Qr/(4\pi\varepsilon_0R^3)$ inside and $E = Q/(4\pi\varepsilon_0r^2)$ outside.

Your tasks.

1. In wire_field, return the field in N/C. lam is in nC/m and r is in m.
2. In sheet_field, return the field in N/C. sigma is in nC/m².
3. In ball_field, return the field in N/C. Q is in nC, and R and r are in m. It must work for a point inside the ball and for a point outside it.