A conducting thick spherical shell of radii $$a$$ and $$b$$, with $$b > a$$, has been charged with uniform surface charge density $$-\sigma$$ on the inner and $$+\sigma$$ on the outer surfaces. Then

A

the net charge on the spherical shell is zero.

B

the radial electric field outside the shell is $$E=\frac{\sigma b^2}{\epsilon_0r^2}$$

C

a radial electric field $$E=\frac{\sigma(b^2-a^2)}{\epsilon_0r^2}$$ exists outside the shell.

D

there is a net electric charge in the cavity equal to $$4\pi\sigma(b^2-a^2)$$