(II) A long pair of insulated wires serves to conduct 24.5 A...

Name: Problem 40, Chapter 20: Physics: Principles with Applications
Uploaded: 2019-05-03T22:30:25-08:00
Duration: 3 min 48 s
Channel: Kyle Godbey
Description: (II) A long pair of insulated wires serves to conduct 24.5 A of dc current to and from an instrument. If the wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.0 cm from their midpoint, in their plane (Fig.20-57)? Compare to the magnetic field of the Earth. FIGURE 20-57 Problems 40 and 41 . (CANT COPY FIGURE)

(II) A long pair of insulated wires serves to conduct 24.5 A of dc current to and from an instrument. If the wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.0 cm from their midpoint, in their plane (Fig.20-57)? Compare to the magnetic field of the Earth. FIGURE 20-57 Problems 40 and 41 . (CANT COPY FIGURE)

(II) A long pair of insulated wires serves to conduct 24.5 A of dc current to and from an instrument. If the wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.0 cm from their midpoint, in their plane (Fig.20-57)? Compare to the magnetic field of the Earth.
FIGURE 20-57 Problems 40 and 41 . (CANT COPY FIGURE)

Key Concepts

Magnetic Field from a Current-Carrying Conductor

A long, straight conductor carrying a steady current produces a magnetic field in the surrounding space. The magnitude of this field at any point a perpendicular distance r from the wire is given by the equation B = ??I/(2?r), where ?? is the permeability of free space and I is the current. This concept is fundamental to understanding how moving charges create magnetic fields and underpins many calculations in electromagnetism.

Superposition Principle in Electromagnetism

When dealing with multiple current-carrying conductors, the total magnetic field at any point is the vector sum of the fields produced by each conductor individually. This principle of superposition allows for the calculation of complex field configurations by adding the contributions from each source, taking into account both their magnitudes and directions.

Ampère's Law

Ampère's Law is a fundamental law of magnetism which relates the integrated magnetic field around a closed loop to the electric current passing through the loop. It provides a powerful method for calculating magnetic fields in cases with high symmetry, such as the field around a long straight conductor, and reinforces the relationship between currents and the magnetic fields they generate.

Comparison with the Earth's Magnetic Field

The Earth's magnetic field, which is typically on the order of tens of microteslas, serves as a common reference point when evaluating the magnitude of laboratory-generated magnetic fields. Understanding how the magnetic field produced by a current-carrying conductor compares with the Earth's field can provide context for the strength and practical significance of the calculated values.

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