A uniformly charged disk of radius 35.0 cm carries charge with a density of 7.90 ×10^-3 C / m^2

step 1 Okay, so this is the equation for the electric view on the axis of the disk, which is equal to 2

A uniformly charged disk of radius 35.0 cm carries charge...

A uniformly charged disk of radius 35.0 $\mathrm{cm}$ carries charge with a density of $7.90 \times 10^{-3} \mathrm{C} / \mathrm{m}^{2}$ . Calculate the electric field on the axis of the disk at (a) $5.00 \mathrm{cm},$ (b) $10.0 \mathrm{cm},$ (c) $50.0 \mathrm{cm},$ and $(\mathrm{d}) 200 \mathrm{cm}$ from the center of the disk.

Key Concepts

Integration in Electrostatics

In cases where the electric field is generated by a continuous charge distribution, one typically employs integration to sum the contributions from individual charge elements. This method considers the vector addition of the fields produced by each charge element and is essential for obtaining the net electric field when symmetry does not allow a direct application of Gauss’s Law.

Electric Field on the Axis

The electric field on the axis of a uniformly charged disk is obtained by summing up the contributions from each infinitesimal charge element on the disk. Owing to the symmetry about the central axis, only the axial components of the electric field from each element survive, leading to an integral that results in a simplified formula for the on-axis field as a function of the charge density, the disk’s radius, the axial distance, and the permittivity of free space.

Surface Charge Density

Surface charge density, usually denoted by ?, represents the amount of charge per unit area on the disk. It is a fundamental parameter in problems involving charge distributions, as it directly relates the total charge on the surface to the area, and is a key factor in determining the magnitude of the electric field generated by the disk.

Uniform Charge Distribution

A uniform charge distribution means that the total charge is spread evenly over the entire surface of the disk. This uniformity allows for the use of symmetry in calculations, which simplifies the process of determining the resulting electric field by ensuring that contributions from different regions of the disk can be combined in a systematic way.

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