College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Question
Find the electric field a distance z from the center of a spherical surface of radius R (See attatched figure) that carries a uniform charge density σ . Treat the case z < R (inside) as well as z > R (outside). Express your answers in terms of the total charge q on the sphere.
(Hint: Use the law of cosines to write r (script) in terms of R and θ . Be sure to take the positive square root: √(R2+z2−2Rz) = (R−z) if R > z, but it’s (z − R) if R < z.)
Transcribed Image Text:This image represents a three-dimensional coordinate system with a sphere centered at the origin. Within this system, several key elements are depicted:
1. **Axes:**
- The x-axis is represented horizontally in the plane of the page.
- The y-axis is also horizontal and perpendicular to the x-axis, extending horizontally but not visible due to the perspective.
- The z-axis is vertical, extending upwards from the origin.
2. **Sphere:** A sphere is centered at the origin (0,0,0) within the coordinate system.
3. **Point P:** Labeled point "P" is located on the surface of the sphere. A line extends from the origin to this point.
4. **Radius (R):** The line from the center of the sphere to point P represents the radius (R) of the sphere.
5. **Angle (θ):** An angle θ is shown between the radius R and the vertical z-axis. This is typically used to demonstrate spherical coordinates or angles in a polar coordinate system.
6. **Normal Vector (n):** A vector labeled "n" is shown extending perpendicularly from the surface of the sphere at point P. This vector represents the normal to the surface of the sphere at that point.
This diagram is often used to illustrate concepts in geometry, physics, and engineering related to spherical coordinates and vector analysis.
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