Moderate# Electric Field due to a Charged Disk: Using Symmetry

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The figure below shows a disk of radius $R$ with a uniform surface charge density $\sigma$. We are interested in the electric field at a distance $d$ along a perpendicular line from the center of the disk of charge. In order to set up the problem, and to ultimately find the vector electric field at $d$, consider the ring at radius $r$ with width $dr$.

The charge in this circular region will result in an electric field, $\vec E_r$ at the distance $d$ along the center line perpendicular to the disk.

Which of the expressions below describes the **vector** field due to the ring of charge? Be sure to use symmetry to determine which components of the electric field add and which cancel.