Problem $2\mathrm{.}4$

$(10$ marks$)$

A circular ring with a uniform charge distribution is placed with its plane on the $\backslash ($ x y $\backslash )$ plane.

A$.$ Use Gauss's law to find the electric field inside the ring.

B$.$ Repeat A$)$ If the ring is immersed in a linear dielectric.

Hint: Note that if we add two rings at equal distances away, the electric field inside the ring will not change.