Infinite Wire
Infinite Wire - Related Videos
09:17
Hot Wire Anemometry
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2023
Source: Ricardo Mejia-Alvarez and Hussam Hikmat Jabbar, Department of Mechanical Engineering, Michigan State University, East Lansing, MI Hot-wire anemometers have a very short time-response, which makes them ideal to measure rapidly fluctuating phenomena such as turbulent flows. The purpose of this experiment is to demonstrate the use of hot-wire anemometry.
01:28
Introduction to Infinite Series
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2026
An infinite series is the sum of an infinite sequence of terms. Instead of adding only a fixed number of values, the addition continues without end. To make sense of this process, mathematicians examine partial sums, which are running totals formed by adding the first few terms of the series. If these partial sums approach a fixed number, the infinite series is said to converge. If they do not approach a finite value, the series diverges.The water tank example illustrates convergence through...
01:28
Infinitely Repeated Games
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2025
An infinitely repeated game is a scenario where players repeatedly engage in the same game without a predetermined end. This concept is crucial in understanding long-term interactions in various fields of the social sciences, including economics and international relations. Examples: Firms Setting Prices: Companies continuously adjust prices. Trade Negotiations: Countries consistently negotiate trade terms. Tit-for-Tat Strategy Cooperative Start: Players begin with a cooperative action,...
07:28
A Contusive Model of Unilateral Cervical Spinal Cord Injury Using the Infinite Horizon Impactor
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Cited by 46 •
2012
A reliable and repeatable way to produce a cervical unilateral spinal cord injury using the Infinite Horizon impactor is described. The method takes advantage of a custom designed frame and clamp to stabilize the spine. The standardized procedure and biomechanical injury parameters result in sufficient and sustained injuries.
01:29
Improper Integrals: Infinite Intervals
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2026
An integral is classified as improper due to an infinite interval when at least one of its limits of integration extends to positive or negative infinity. In such cases, the region under the curve is unbounded, and standard techniques for evaluating definite integrals are not directly applicable. Instead, the improper integral is defined through a limiting process that allows one to determine whether the accumulated area remains finite despite the infinite domain.Application to Exponential...
FAQs
Cylindrical symmetry means that points at the same radial distance from the wire are equivalent for the field calculation. The magnetic field therefore depends on distance from the wire rather than on angular position along a circular path. This uniformity allows Ampère’s law to relate the field around the path directly to the steady current passing through it.
The magnetic field becomes weaker as radial distance increases. For a steady current, Ampère’s law gives the inverse-distance relationship B = μ₀I/(2πr), where I is the current and r is the distance from the wire. Consequently, doubling the distance reduces the field magnitude by half while leaving its circular direction unchanged.
Point the thumb of your right hand in the direction of conventional current, and the curled fingers indicate the magnetic-field direction around the conductor. Reversing the current reverses the field circulation. This rule identifies orientation, while Ampère’s law supplies the magnitude, so both are needed for a complete field description.
The charged-wire model describes an electrostatic electric field produced by an infinitely long line charge, whereas the current-carrying model describes a magnetic field generated by steady motion of charge. In both cases, cylindrical symmetry makes the field depend on radial distance. Separating the two models prevents electric-field and magnetic-field predictions from being conflated.
First identify the steady current and the circular path centered on the wire. Cylindrical symmetry makes the magnetic-field magnitude uniform along that path, so the field can be related to the current enclosed by it through Ampère’s law. Evaluating the resulting relationship at a chosen radius gives the field magnitude and its radial dependence.
The approximation is useful when a straight conductor is sufficiently long that end effects can be neglected over the region of interest. It provides an analytical reference for interpreting laboratory measurements and for analyzing cables, coils, and transmission systems. Comparing measured or modeled fields with this ideal result helps assess how closely a real arrangement follows the assumed symmetry.