You hold a circular loop of wire at the north magnetic pole...

Name: Problem 85, Chapter 23: Pearson Physics
Uploaded: 2023-02-25T14:29:42-08:00
Duration: 3 min 43 s
Channel: Vishal Gupta
Description: You hold a circular loop of wire at the north magnetic pole of the Earth. Consider the magnetic flux through this loop due to Earth's magnetic field. Is the flux when the normal to the loop is horizontal greater than, less than, or equal to the flux when the normal is vertical? Explain.

You hold a circular loop of wire at the north magnetic pole of the Earth. Consider the magnetic flux through this loop due to Earth's magnetic field. Is the flux when the normal to the loop is horizontal greater than, less than, or equal to the flux when the normal is vertical? Explain.

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Key Concepts

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given surface. It is defined as the product of the magnetic field strength, the area, and the cosine of the angle between the field direction and the perpendicular (normal) to the surface, capturing how effectively the field permeates the surface.

Orientation and Angle Dependency

The amount of flux through a surface is highly dependent on the orientation of the surface relative to the magnetic field. When the surface’s normal is aligned (parallel) with the magnetic field, the cosine of the angle is maximized, leading to maximum flux. Conversely, if the surface is oriented such that the normal is perpendicular to the field, the cosine factor decreases, and so does the flux.

Dot Product in Flux Calculation

The mathematical expression for magnetic flux involves the dot product between the magnetic field vector and the area vector of the surface. This calculation inherently accounts for both the magnitude of the field and its directional relation to the surface, emphasizing the role of the cosine of the angle between them.

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