A uniformly charged disc of radius $R$ having surface charge density $\sigma$ is placed in the $xy$ plane with its center at the origin. Find the electric field intensity along the $z$-axis at a distance $Z$ from origin:

• A

  $E=\frac{2{\epsilon }_0}{\sigma }\left(\frac{1}{{\left(Z^2+R^2\right)}^{1/2}}+Z\right)$
• B

  $E=\frac{\sigma }{2{\epsilon }_0}\left(1+\frac{Z}{{\left(Z^2+R^2\right)}^{1/2}}\right)$
• Correct answer
  C

  $E=\frac{\sigma }{2{\epsilon }_0}\left(1-\frac{Z}{{\left(Z^2+R^2\right)}^{1/2}}\right)$
• D

  $E=\frac{\sigma }{2{\epsilon }_0}\left(\frac{1}{\left(Z^2+R^2\right)}+\frac{1}{Z^2}\right)$

Hence, the correct answer is option: 'C'.