Question

Explain qualitatively how it is possible for the electric field at locations near the center of a uniformly charged disk not to vary with distance away from the disk.

Short answer

The electric field at locations near the center of a uniformly charged disk does not vary with distance because with respect to these points the disk behaves like an infinite charged sheet.

Step-by-step solution

Identification of given data

A uniformly charged disk.

Field due to an infinite uniformly charged sheet

The electric field due to an infinitely long uniformly charged disk is constant and does not vary with distance from the sheet.

Determination of the variation of electric field near the centre of a uniformly charged disk

For points very close to the centre of a uniformly charged disk, the distance of the points from the disk are negligible compared to the dimension of the disk. Hence with respect to these points, the disk behaves like an infinite sheet, the field due to which is constant. Thus, the electric field measured at such points do not vary much with distance from the disk.