Charged disk: A thin, circular disk of radius 30.0 cm is oriented in the yz-plane with its center at the origin. The disk carries a total charge of +3.00 μC distributed uniformly over its surface. Calculate the magnitude of the electric field due to the disk at the point x = 15.0 cm along the x-axis. (ε₀ = 8.85 × 10^-12 C²/N ∙ m²) A) 9.95 × 10⁵ N/C B) 4.98 × 10⁵ N/C C) 3.31 × 10⁵ N/C D) 2.49 × 10⁵ N/C E) 1.99 × 10⁵ N/C

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Quizplus · Accepted Answer

The electric field due to a uniformly charged disk at a point along its axis can be calculated using the formula $E = \frac{\sigma}{2\epsilon_0} \left(1 - \frac{x}{\sqrt{x^2 + R^2}}\right)$, where $\sigma$ is the surface charge density ($\sigma = \frac{Q}{\pi R^2}$), $Q$ is the total charge, $R$ is the radius of the disk, $x$ is the distance from the center of the disk to the point where the electric field is being calculated, and $\epsilon_0$ is the permittivity of free space ($8.85 \times 10^{-12} C^2/N \cdot m^2$). Plugging in the given values ($Q = 3.00 \mu C = 3.00 \times 10^{-6} C$, $R = 30.0 cm = 0.30 m$, $x = 15.0 cm = 0.15 m$), we find the electric field magnitude at the specified point.

Charged Disk: a Thin, Circular Disk of Radius 30