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

Name: Problem 75, Chapter 23: Physics
Uploaded: 2020-06-13T15:30:24-08:00
Duration: 1 min 16 s
Channel: Sanjeev Kumar
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 the Earth's magnetic field. Is the flux when the normal to the loop points horizontally greater than, less than, or equal to the flux when the normal points vertically downward? 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 the Earth's magnetic field. Is the flux when the normal to the loop points horizontally greater than, less than, or equal to the flux when the normal points vertically downward? Explain.

Key Concepts

Magnetic Flux

Magnetic flux measures the amount of magnetic field passing through a given area. It is defined as the surface integral of the magnetic field over an area, typically expressed as ? = B · A, where B is the magnetic field vector and A is the vector representing the area of the loop. This concept is central to understanding how different orientations of a loop affect the flux it experiences.

Dot Product and Angle Dependence

The use of a dot product in calculating magnetic flux introduces a dependence on the cosine of the angle between the magnetic field vector and the normal vector of the loop's surface. This means the flux is maximized when the field and the area are aligned and decreases as the angle between them increases.

Loop Orientation

The orientation of the loop’s normal relative to the magnetic field is crucial. Changing the loop’s orientation alters the cosine factor in the flux equation, thereby changing the effective component of the magnetic field that passes through the loop. This principle explains how different orientations, such as horizontal versus vertical normals, result in different magnetic flux values.

Magnetic Field Geometry

Understanding the geometry of the magnetic field, especially as it pertains to natural fields like Earth’s, is important. In regions where the magnetic field lines are not parallel to the surface, the relative alignment with a loop’s normal vector can greatly influence the measured flux, emphasizing the role of both field direction and loop orientation in electromagnetic analysis.

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