A rectangular area is rotated in a uniform electric field,...

Name: Problem 62, Chapter 16: College Physics
Uploaded: 2021-08-11T07:43:03-08:00
Duration: 1 min 15 s
Channel: Prabhu Ramji
Description: A rectangular area is rotated in a uniform electric field, from a position where the maximum electric flux goes through it to an orientation where only half the maximum flux goes through it. What is the angle of rotation?

A rectangular area is rotated in a uniform electric field, from a position where the maximum electric flux goes through it to an orientation where only half the maximum flux goes through it. What is the angle of rotation?

Key Concepts

Uniform Electric Field

A uniform electric field has the same magnitude and direction at every point within the region considered. This characteristic simplifies flux calculations, as it allows for direct multiplication of the field strength by the area (and the cosine factor) without concern for spatial variations in the field.

Electric Flux

Electric flux is a measure of how much of the electric field passes through a given area. It is calculated by taking the dot product of the electric field vector and the area vector, which depends on both the magnitude of the field and the orientation of the surface relative to the field.

Cosine Relationship in Flux

The electric flux through a surface is given by the formula ? = EA cos(?), where E is the magnitude of the electric field, A is the area of the surface, and ? is the angle between the electric field direction and the normal to the surface. This cosine dependence explains how rotation of the surface reduces the flux by the factor cos(?).

Rotation of a Surface in an Electric Field

When a surface is rotated in a uniform electric field, its orientation with respect to the field changes. This rotation affects the electric flux through the surface because the effective component of the area perpendicular to the field is modified by the cosine of the rotation angle, which is crucial for determining how much the flux is reduced.

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